{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HpRtgWwprG72"
   },
   "source": [
    "# **`Chapter 2: Special Discrete Random Variables`**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "DHZIzu1stgEF"
   },
   "source": [
    "**Table of Content:**\n",
    "\n",
    "- [Import Libraries](#Import_Libraries)\n",
    "- [2.1. Bernoulli Distribution](#Bernoulli_Distribution)\n",
    "- [2.2. Binomial Distribution](#Binomial_Distribution)\n",
    "- [2.3. Negative Binomial (Pascal) Distribution](#Negative_Binomial_Distribution)\n",
    "- [2.4. Geometric Distribution](#Geometric_Distribution)\n",
    "- [2.5. Poisson Distribution](#Poisson_Distribution)\n",
    "- [2.6. Discrete Uniform Distribution](#Discrete_Uniform_Distribution)\n",
    "- [2.7. Hypergeometric Distribution](#Hypergeometric_Distribution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "WJhmgDxsVHEO"
   },
   "source": [
    "<a name='Import_Libraries'></a>\n",
    "\n",
    "## **Import Libraries**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "vXStgb2JU6c0",
    "outputId": "8195a0a1-6093-4e60-c038-e78e34aa0050"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: scipy in c:\\anaconda\\lib\\site-packages (1.11.2)\n",
      "Requirement already satisfied: numpy<1.28.0,>=1.21.6 in c:\\anaconda\\lib\\site-packages (from scipy) (1.24.3)\n"
     ]
    }
   ],
   "source": [
    "!pip install --upgrade scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ZPuphzTmU-P8",
    "outputId": "1bc3dbb9-3a13-42f3-e297-12dededee46b"
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as mpatches\n",
    "import seaborn as sns\n",
    "import math\n",
    "from scipy import stats\n",
    "from scipy.stats import norm\n",
    "from scipy.stats import chi2\n",
    "from scipy.stats import t\n",
    "from scipy.stats import f\n",
    "from scipy.stats import bernoulli\n",
    "from scipy.stats import binom\n",
    "from scipy.stats import nbinom\n",
    "from scipy.stats import geom\n",
    "from scipy.stats import poisson\n",
    "from scipy.stats import uniform\n",
    "from scipy.stats import randint\n",
    "from scipy.stats import nbinom\n",
    "from scipy.stats import expon\n",
    "from scipy.stats import gamma\n",
    "from scipy.stats import beta\n",
    "from scipy.stats import weibull_min\n",
    "from scipy.stats import hypergeom\n",
    "from scipy.stats import shapiro\n",
    "from scipy.stats import pearsonr\n",
    "from scipy.stats import normaltest\n",
    "from scipy.stats import anderson\n",
    "from scipy.stats import spearmanr\n",
    "from scipy.stats import kendalltau\n",
    "from scipy.stats import chi2_contingency\n",
    "from scipy.stats import ttest_ind\n",
    "from scipy.stats import ttest_rel\n",
    "from scipy.stats import mannwhitneyu\n",
    "from scipy.stats import wilcoxon\n",
    "from scipy.stats import kruskal\n",
    "from scipy.stats import friedmanchisquare\n",
    "from statsmodels.tsa.stattools import adfuller\n",
    "from statsmodels.tsa.stattools import kpss\n",
    "from statsmodels.stats.weightstats import ztest\n",
    "from scipy.integrate import quad\n",
    "from IPython.display import display, Latex\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "warnings.simplefilter(action='ignore', category=FutureWarning)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5z2nOmnTrKxu"
   },
   "source": [
    "<a name='Bernoulli_Distribution'></a>\n",
    "\n",
    "## **2.1. Bernoulli Distribution:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0riBQ6Kwr91-"
   },
   "source": [
    "Suppose that an experiment, whose outcome can be classified as either a “success” or as a “failure” is performed. If we let $X = 1$ when the outcome is a success and $X = 0$ when it is a failure, then the probability mass function of $X$ is given by:\n",
    "\n",
    "$P(X=x) =\\begin{cases}p & x = 1\\\\1-p = q & x = 0\\end{cases}$\n",
    "\n",
    "or\n",
    "\n",
    "$P(X=x) = p^x(1-p)^{1-x} \\quad \\quad x = 0,1$\n",
    "\n",
    "$\\\\ $\n",
    "\n",
    "$E(X) = p$\n",
    "\n",
    "$Var(X) = p(1-p)$\n",
    "\n",
    "$Median(X) = \\begin{cases}0 & p < \\frac{1}{2}\\\\{[0,1]} & p = \\frac{1}{2} \\\\1 & p > \\frac{1}{2}\\end{cases}$\n",
    "\n",
    "$Mode(X) = \\begin{cases}0 & p < \\frac{1}{2}\\\\{[0,1]} & p = \\frac{1}{2} \\\\1 & p > \\frac{1}{2}\\end{cases}$\n",
    "\n",
    "$Skewness(X) = \\frac{1-2p}{\\sqrt{p(1-p)}}$\n",
    "\n",
    "$Kurtosis(X) = \\frac{6p^2-6p+1}{p(1-p)} = \\frac{1-6pq}{p(1-p)}$\n",
    "\n",
    "$\\\\ $\n",
    "\n",
    "Moment-generating function:\n",
    "\n",
    "$M_{x}(t) = p\\ e^t + q$\n",
    "\n",
    "$\\\\ $\n",
    "\n",
    "$CDF = F(X=x) = \\begin{cases}0 & x < 0\\\\1-p & 0\\leq x< 1 \\\\1 & x > 0\\end{cases}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 290
    },
    "id": "l0MqQdPqrnPe",
    "outputId": "2292e925-93dc-4677-8cf7-321e2dea23cd"
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "N = 1000000\n",
    "p = 0.8\n",
    "\n",
    "ber_data = np.random.binomial(n = 1, p = p, size = N)\n",
    "\n",
    "sns.histplot(ber_data, color='b', stat='density', bins=50)\n",
    "plt.xlim(-0.1,1.1)\n",
    "plt.xticks([0,1], fontsize=20, ha='center')\n",
    "plt.title(f'Bernoulli Distribution ({p})');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "zU4alj0sutS2",
    "outputId": "157bdf0d-39d9-42b9-acb9-a922921adf60"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the Bernoulli(P=0.8) Distribution is:  0.8\n",
      "The median of the Bernoulli(P=0.8) Distribution is:  1.0\n",
      "The variance of the Bernoulli(P=0.8) Distribution is:  0.16\n",
      "The standard deviation of the Bernoulli(P=0.8) Distribution is:  0.4\n",
      "The skewness of the Bernoulli(P=0.8) Distribution is:  -1.5\n",
      "The kurtosis of the Bernoulli(P=0.8) Distribution is:  0.25\n"
     ]
    }
   ],
   "source": [
    "p = 0.8\n",
    "print(f'The mean of the Bernoulli(P={p}) Distribution is: ', np.round(bernoulli.mean(p = p), 4))\n",
    "print(f'The median of the Bernoulli(P={p}) Distribution is: ', np.round(bernoulli.median(p = p), 4))\n",
    "print(f'The variance of the Bernoulli(P={p}) Distribution is: ', np.round(bernoulli.var(p = p), 4))\n",
    "print(f'The standard deviation of the Bernoulli(P={p}) Distribution is: ', np.round(bernoulli.std(p = p), 4))\n",
    "print(f'The skewness of the Bernoulli(P={p}) Distribution is: ', np.round(bernoulli.stats(p, moments='mvsk')[2], 4))\n",
    "print(f'The kurtosis of the Bernoulli(P={p}) Distribution is: ', np.round(bernoulli.stats(p, moments='mvsk')[3], 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NsyayQJ1J2Bj"
   },
   "source": [
    "Integrating the PDF, gives us the cumulative distribution function (CDF) which is a function that maps values to their percentile rank in a distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "id": "r1BuJBNjaj0M",
    "outputId": "424dcada-031b-46da-eb21-e9bf004ce730"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0, 1.99, 0.001)\n",
    "x1 = np.arange(0, 2)\n",
    "x2 = np.arange(0, 1) + 0.999\n",
    "\n",
    "plt.scatter(x, bernoulli.cdf(x, p=p), color = 'r')\n",
    "plt.scatter(x2, bernoulli.cdf(x2, p=p), color = 'white', edgecolor='black', s=100)\n",
    "plt.scatter(x1, bernoulli.cdf(x1, p=p), color = 'black', edgecolor='black', s=100)\n",
    "plt.xlim(-0.05,2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "4IAqcmYESSAS"
   },
   "source": [
    "To find the left probability of a point use the code below:\n",
    "\n",
    "''\n",
    "bernoulli.cdf($X,P$)\n",
    "''\n",
    "\n",
    "To find the right probability of a point use the code below:\n",
    "\n",
    "''\n",
    "bernoulli.sf($X,P$)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Zm-zmsdNSa_z",
    "outputId": "e64d5b74-f8f7-497e-9548-71a609c62de1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The left probability of *0.5* in the B(0.2) Distribution is:  0.8\n",
      "The Right probability of *0.5* in the B(0.2) Distribution is:  0.2\n"
     ]
    }
   ],
   "source": [
    "X = 0.5\n",
    "p = 0.2\n",
    "print(f'The left probability of *{X}* in the B({p}) Distribution is: ', bernoulli.cdf(X, p=p))\n",
    "print(f'The Right probability of *{X}* in the B({p}) Distribution is: ', bernoulli.sf(X, p=p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jir0-E5gTNRb"
   },
   "source": [
    "To find the probability of a point use the code below:\n",
    "\n",
    "''\n",
    "bernoulli.pmf($X,P$)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "srUdo4jMTPqT",
    "outputId": "16ffcee6-ff7d-4200-c4f0-b51f4c5ae830"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of *X=1* in the B(0.2) Distribution is:  0.2\n"
     ]
    }
   ],
   "source": [
    "X = 1\n",
    "p = 0.2\n",
    "print(f'The probability of *X={X}* in the B({p}) Distribution is: ', bernoulli.pmf(X, p=p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fFKKuULM2F16"
   },
   "source": [
    "If $X \\sim Ber(P) \\quad$ then $\\quad Y_1 = X^n \\sim Ber(P)$\n",
    "\n",
    "If $X \\sim Ber(P) \\quad$ then $\\quad Y_2 = 1-X \\sim Ber(1-P)$\n",
    "\n",
    "If $X \\sim Ber(P) \\quad$ then $\\quad Y_3 = 1-X^n \\sim Ber(1-P)$\n",
    "\n",
    "If $X \\sim Ber(P) \\quad$ then $\\quad Y_4 = {(1-X)}^n \\sim Ber(1-P)$\n",
    "\n",
    "If $X_1, X_2, ..., X_n \\sim Ber(P) \\quad$ then $\\quad Y_5 = Min(X_1, X_2, ..., X_n) \\sim Ber(P^n)$\n",
    "\n",
    "If $X_1, X_2, ..., X_n \\sim Ber(P) \\quad$ then $\\quad Y_6 = Max(X_1, X_2, ..., X_n) \\sim Ber(1-q^n)$\n",
    "\n",
    "If $X_1, X_2, ..., X_n \\sim Ber(P) \\quad$ then $\\quad Y_7 = X_1 \\times X_2\\times ...\\times X_n \\sim Ber(P^n)$\n",
    "\n",
    "If $Y_1 = Min(X_1, X_2, ..., X_n), Y_2 = Max(X_1, X_2, ..., X_n) \\quad$ then $\\quad Y_8 = {Y_1}{Y_2} \\sim Ber(P^n)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "c1_c9ACB5Q_j"
   },
   "source": [
    "<a name='Binomial_Distribution'></a>\n",
    "\n",
    "## **2.2. Binomial Distribution:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8m2i2g8D5hvP"
   },
   "source": [
    "Suppose now that $n$ independent trials, each of which results in a “success” with probability $p$ and in a “failure” with probability $1 − p$, are to be performed. If $X$ represents the number of successes that occur in the $n$ trials, then $X$ is said to be a binomial random variable with parameters $(n, p)$.\n",
    "\n",
    "$P(X=i) = \\binom{i}{n} p^i (1-p)^{n-i} \\quad \\quad x = 0,1,...,n$\n",
    "\n",
    "$\\\\ $\n",
    "\n",
    "$E(X) = np$\n",
    "\n",
    "$Var(X) = np(1-p)$\n",
    "\n",
    "$Skewness(X) = \\frac{q-p}{\\sqrt{npq}}$\n",
    "\n",
    "$Kurtosis(X) = \\frac{1-6pq}{npq}$\n",
    "\n",
    "$Mode(X) = \\begin{cases}(n+1)p,(n+1)p-1 & if(n+1)p \\in integer \\\\ [(n+1)p] & if(n+1)p \\not\\in integer \\end{cases}$\n",
    "\n",
    "$\\\\ $\n",
    "\n",
    "Moment-generating function:\n",
    "\n",
    "$M_{x}(t) = (pe^t + q)^n$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "MqmeyCON5Vjz",
    "outputId": "d0a14a8e-2a0b-4809-e964-56218576dce6"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "N = 1000000\n",
    "n, p = [10, 0.5]\n",
    "\n",
    "binom_data = np.random.binomial(n = n, p = p, size = N)\n",
    "\n",
    "sns.histplot(binom_data, color='olive', stat='density', bins=50)\n",
    "\n",
    "plt.xlim(0,n)\n",
    "plt.xticks(list(range(0,n+1)), fontsize=12, ha='center')\n",
    "plt.title('Binomial Distribution');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "EBZQYYcA5Jdb"
   },
   "outputs": [],
   "source": [
    "def mode_binom(n,p):\n",
    "  if math.modf((n+1)*p)[0] == 0.0:\n",
    "    return (n+1)*p, (n+1)*p-1\n",
    "  else:\n",
    "    return np.floor((n+1)*p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "jj8DJCi2945b",
    "outputId": "1027024c-1486-464f-cdad-2ed6805797eb"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the B(10,0.5) Distribution is:  5.0\n",
      "The median of the B(10,0.5) Distribution is:  5.0\n",
      "The variance of the B(10,0.5) Distribution is:  2.5\n",
      "The standard deviation of the B(10,0.5) Distribution is:  1.5811\n",
      "The mode of the B(10,0.5) Distribution is:  5.0\n",
      "The skewness of the B(10,0.5) Distribution is:  0.0\n",
      "The kurtosis of the B(10,0.5) Distribution is:  -0.2\n"
     ]
    }
   ],
   "source": [
    "n, p = [10, 0.5]\n",
    "print(f'The mean of the B({n},{p}) Distribution is: ', np.round(binom.mean(p = p, n = n), 4))\n",
    "print(f'The median of the B({n},{p}) Distribution is: ', np.round(binom.median(p = p, n = n), 4))\n",
    "print(f'The variance of the B({n},{p}) Distribution is: ', np.round(binom.var(p = p, n = n), 4))\n",
    "print(f'The standard deviation of the B({n},{p}) Distribution is: ', np.round(binom.std(p = p, n = n), 4))\n",
    "print(f'The mode of the B({n},{p}) Distribution is: ', np.round(mode_binom(p = p, n = n), 4))\n",
    "print(f'The skewness of the B({n},{p}) Distribution is: ', np.round(binom.stats(p = p, n = n, moments='mvsk')[2], 4))\n",
    "print(f'The kurtosis of the B({n},{p}) Distribution is: ', np.round(binom.stats(p = p, n = n, moments='mvsk')[3], 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6KM1kHTxJoHG"
   },
   "source": [
    "Integrating the PDF, gives us the cumulative distribution function (CDF) which is a function that maps values to their percentile rank in a distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "id": "dzB3koSeKxkX",
    "outputId": "0a116722-a611-4778-8467-6d63dcf98e5b"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0, n, 0.001)\n",
    "x1 = np.arange(0, n)\n",
    "x2 = np.arange(0, n-1) + 0.999\n",
    "\n",
    "plt.scatter(x, binom.cdf(x, p=p, n=n), color = 'r')\n",
    "plt.scatter(x2, binom.cdf(x2, p=p, n=n), color = 'white', edgecolor='black', s=100)\n",
    "plt.scatter(x1, binom.cdf(x1, p=p, n=n), color = 'black', edgecolor='black', s=100)\n",
    "plt.xlim(0,n);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "InSCdsjR9xEC"
   },
   "source": [
    "The binomial distribution histogram depends on the $n$ and $p$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 356
    },
    "id": "zk5PfeVlDJxh",
    "outputId": "c29d8aad-c7d2-4f65-b27c-d205d7666eca"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n1, n2, n3 = [9, 10, 10]\n",
    "p1, p2, p3 = [0.2, 0.8,0.5]\n",
    "\n",
    "fig, axes = plt.subplots(1, 3, figsize=(15, 5), sharey=True)\n",
    "fig.suptitle('Binomial Distribution')\n",
    "\n",
    "sns.histplot(ax=axes[0], x=np.random.binomial(n = n1, p = p1, size = N),  bins=50, color = '#A1C935')\n",
    "axes[0].set_title(f'B({n1},{p1})')\n",
    "\n",
    "sns.histplot(ax=axes[1], x=np.random.binomial(n = n2, p = p2, size = N),  bins=50, color = '#1AEACD')\n",
    "axes[1].set_title(f'B({n2},{p2})')\n",
    "\n",
    "sns.histplot(ax=axes[2], x=np.random.binomial(n = n3, p = p3, size = N),  bins=50, color = '#F75D59')\n",
    "axes[2].set_title(f'B({n3},{p3})');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pszDBGvEUJD5"
   },
   "source": [
    "To find the left probability of a point use the code below:\n",
    "\n",
    "''\n",
    "binom.cdf($X,P,n$)\n",
    "''\n",
    "\n",
    "To find the right probability of a point use the code below:\n",
    "\n",
    "''\n",
    "binom.sf($X,P,n$)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "uViuxJsKUJD6",
    "outputId": "aed3bd6c-5d97-4dd1-de83-be2cafa4d784"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The left probability of *2* in the B(10,0.2) Distribution is:  0.6777995263999997\n",
      "The Right probability of *2* in the B(10,0.2) Distribution is:  0.32220047360000026\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "n, p = [10, 0.2]\n",
    "print(f'The left probability of *{X}* in the B({n},{p}) Distribution is: ', binom.cdf(X, p=p, n=n))\n",
    "print(f'The Right probability of *{X}* in the B({n},{p}) Distribution is: ', binom.sf(X, p=p, n=n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-rESDu9IkKYS"
   },
   "source": [
    "To find the probability between two points $[X,Y]$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "h66sd6eZkLcF",
    "outputId": "c3de1580-a02b-47fe-9e39-a7a8d90f2f8b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *[2, 4]* in the B(10,0.2) Distribution is:  0.5913968639999998\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "Y = 4\n",
    "n, p = [10, 0.2]\n",
    "xs = np.arange(X, Y+1)\n",
    "print(f'The probability between *[{X}, {Y}]* in the B({n},{p}) Distribution is: ', np.sum([binom.pmf(xs, p=p, n=n) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "Ryd4pcyI6BYE",
    "outputId": "16010584-ecaf-43d6-98e8-849227385d36"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X))\n",
    "x2 = list(np.arange(X,Y+1))\n",
    "x3 = list(np.arange(Y+1,n+1))\n",
    "plt.bar(x1, binom.pmf(x1, p=p, n=n), color ='gray')\n",
    "plt.bar(x2, binom.pmf(x2, p=p, n=n), color ='#DFFF00')\n",
    "plt.bar(x3, binom.pmf(x3, p=p, n=n), color ='gray')\n",
    "plt.xlim(-1,n+1)\n",
    "plt.xticks(np.arange(0,n+1), fontsize=12, ha='center')\n",
    "plt.title(f'B({n}, {p})')\n",
    "xs = np.arange(X, Y+1)\n",
    "prob = np.sum([binom.pmf(xs, p=p, n=n) for xs in xs])\n",
    "plt.text(7, 0.02, f'$P({np.round(X, 3)} \\leq X \\leq {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "MutW8yZGldq_"
   },
   "source": [
    "To find the probability between two points $(X,Y)$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "M0DxV4XjlnnT",
    "outputId": "94091ac2-8e13-49d8-8883-04fb77c46c57"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *(2, 4)* in the B(10,0.2) Distribution is:  0.20132659199999992\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "Y = 4\n",
    "n, p = [10, 0.2]\n",
    "xs = np.arange(X+1, Y)\n",
    "print(f'The probability between *({X}, {Y})* in the B({n},{p}) Distribution is: ', np.sum([binom.pmf(xs, p=p, n=n) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "FQ-xBNM-_FdA",
    "outputId": "69e00b8c-4bd3-4579-e1f4-77782f2d92b8"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X+1))\n",
    "x2 = list(np.arange(X+1,Y))\n",
    "x3 = list(np.arange(Y,n+1))\n",
    "plt.bar(x1, binom.pmf(x1, p=p, n=n), color ='gray')\n",
    "plt.bar(x2, binom.pmf(x2, p=p, n=n), color ='#DFFF00')\n",
    "plt.bar(x3, binom.pmf(x3, p=p, n=n), color ='gray')\n",
    "plt.xlim(-1,n+1)\n",
    "plt.xticks(np.arange(0,n+1), fontsize=12, ha='center')\n",
    "plt.title(f'B({n}, {p})')\n",
    "xs = np.arange(X+1, Y)\n",
    "prob = np.sum([binom.pmf(xs, p=p, n=n) for xs in xs])\n",
    "plt.text(7, 0.02, f'$P({np.round(X, 3)} < X < {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "xAm4u-pExhO2"
   },
   "source": [
    "To find the probability between two points $[X,Y)$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ozUIQG8bxldK",
    "outputId": "055f57c2-fe05-4ebb-c3ee-53b5c89f6b94"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *[2, 4)* in the B(10,0.2) Distribution is:  0.50331648\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "Y = 4\n",
    "n, p = [10, 0.2]\n",
    "xs = np.arange(X, Y)\n",
    "print(f'The probability between *[{X}, {Y})* in the B({n},{p}) Distribution is: ', np.sum([binom.pmf(xs, p=p, n=n) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "cDfaDGznDL5I",
    "outputId": "8708e1ec-2b75-4926-ddb0-fc17f76f3c94"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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48GBlTgUAAFQDdq1h8fPzk5OTU6nZlOzs7FKzLudLTEzUiBEjtHLlSvXs2fOCfWvUqKF27dpdcIbFzc1Nbm5uFS8eAABUW3bNsLi6uiokJETJyck27cnJyerUqVO5xyUkJOiBBx7Q8uXL1a9fv4u+jmEYSktL07XXXmtPeQAA4Cpl911CkyZN0rBhw9S2bVuFhoZqwYIFSk9P15gxYySdvVSTkZGhxYsXSzobVu6//3699tpr6tixo3V2xsPDQz4+PpKk2NhYdezYUTfeeKPy8vL0+uuvKy0tTXPnzq2q8wQAANWY3YElIiJChw8f1vTp05WZmanmzZsrKSlJQUFBkqTMzEybZ7LMnz9fp0+f1vjx4zV+/Hhr+/Dhw7Vo0SJJ0tGjRzVq1ChlZWXJx8dHrVu31ubNm9W+fftLPD0AAHA1sBiGYTi6iKqQl5cnHx8f5ebmytvb29HlOFRsbKyjS1B0dPQF9+/XxRdpX26NdFV86wNAtVbR39+8lxAAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADC9SgWW+Ph4NW7cWO7u7goJCdGWLVvK7fvhhx+qV69eqlevnry9vRUaGqr169eX6rd69WoFBwfLzc1NwcHBWrNmTWVKAwAAVyG7A0tiYqIiIyM1bdo0paamKiwsTH369FF6enqZ/Tdv3qxevXopKSlJO3bsUPfu3TVgwAClpqZa+6SkpCgiIkLDhg3T999/r2HDhunuu+/Wt99+W/kzAwAAVw2LYRiGPQd06NBBbdq00bx586xtzZo108CBAzVjxowKjXHLLbcoIiJCzz77rCQpIiJCeXl5WrdunbXPbbfdpjp16ighIaFCY+bl5cnHx0e5ubny9va244yuPrGxsY4uQdHR0Rfcv1+WK1RJ+RrJrm99AMBlUNHf3872DHry5Ent2LFDTz75pE17eHi4tm3bVqExiouLlZ+fr7p161rbUlJSNHHiRJt+vXv3VlxcXLnjFBUVqaioyPp5Xl5ehV4fsAfBCgDMwa5LQjk5OTpz5oz8/f1t2v39/ZWVlVWhMWbPnq1jx47p7rvvtrZlZWXZPeaMGTPk4+Nj3QIDA+04EwAAUJ1UatGtxWL7V6dhGKXaypKQkKCYmBglJibqmmuuuaQxo6KilJuba90OHjxoxxkAAIDqxK5LQn5+fnJycio185GdnV1qhuR8iYmJGjFihFauXKmePXva7AsICLB7TDc3N7m5udlTPgAAqKbsmmFxdXVVSEiIkpOTbdqTk5PVqVOnco9LSEjQAw88oOXLl6tfv36l9oeGhpYa8/PPP7/gmAAA4J/DrhkWSZo0aZKGDRumtm3bKjQ0VAsWLFB6errGjBkj6eylmoyMDC1evFjS2bBy//3367XXXlPHjh2tMykeHh7y8fGRJE2YMEFdunTRzJkzdfvtt+ujjz7SF198oa1bt1bVeQIAgGrM7jUsERERiouL0/Tp09WqVStt3rxZSUlJCgoKkiRlZmbaPJNl/vz5On36tMaPH69rr73Wuk2YMMHap1OnTlqxYoXee+89tWzZUosWLVJiYqI6dOhQBacIAACqO7ufw2JWPIfl//AcloqpyO3C1aVOAKiuKvr7m/cSAgAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAApkdgAQAAplepwBIfH6/GjRvL3d1dISEh2rJlS7l9MzMzdc899+jmm29WjRo1FBkZWarPokWLZLFYSm2FhYWVKQ8AAFxl7A4siYmJioyM1LRp05SamqqwsDD16dNH6enpZfYvKipSvXr1NG3aNN16663ljuvt7a3MzEybzd3d3d7yAADAVcjuwDJnzhyNGDFCI0eOVLNmzRQXF6fAwEDNmzevzP6NGjXSa6+9pvvvv18+Pj7ljmuxWBQQEGCzXUhRUZHy8vJsNgAAcHWyK7CcPHlSO3bsUHh4uE17eHi4tm3bdkmFFBQUKCgoSA0aNFD//v2Vmpp6wf4zZsyQj4+PdQsMDLyk1wcAAOZlV2DJycnRmTNn5O/vb9Pu7++vrKysShfRtGlTLVq0SB9//LESEhLk7u6uzp076/fffy/3mKioKOXm5lq3gwcPVvr1AQCAuTlX5iCLxWLzuWEYpdrs0bFjR3Xs2NH6eefOndWmTRu98cYbev3118s8xs3NTW5ubpV+TQAAUH3YNcPi5+cnJyenUrMp2dnZpWZdLqmoGjXUrl27C86wAACAfw67Aourq6tCQkKUnJxs056cnKxOnTpVWVGGYSgtLU3XXnttlY0JAACqL7svCU2aNEnDhg1T27ZtFRoaqgULFig9PV1jxoyRdHZtSUZGhhYvXmw9Ji0tTdLZhbV//fWX0tLS5OrqquDgYElSbGysOnbsqBtvvFF5eXl6/fXXlZaWprlz51bBKQIAgOrO7sASERGhw4cPa/r06crMzFTz5s2VlJSkoKAgSWcfFHf+M1lat25t/XjHjh1avny5goKCtH//fknS0aNHNWrUKGVlZcnHx0etW7fW5s2b1b59+0s4NQAAcLWwGIZhOLqIqpCXlycfHx/l5ubK29vb0eU4VGxsrKNLUHR09AX371flF2lXlUa6+Ld+dakTAKqriv7+5r2EAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6Tk7uoDqJjY21tElKDo62tElAABwRTHDAgAATI/AAgAATI/AAgAATI/AAgAATK9SgSU+Pl6NGzeWu7u7QkJCtGXLlnL7ZmZm6p577tHNN9+sGjVqKDIyssx+q1evVnBwsNzc3BQcHKw1a9ZUpjQAAHAVsjuwJCYmKjIyUtOmTVNqaqrCwsLUp08fpaenl9m/qKhI9erV07Rp03TrrbeW2SclJUUREREaNmyYvv/+ew0bNkx33323vv32W3vLAwAAVyG7A8ucOXM0YsQIjRw5Us2aNVNcXJwCAwM1b968Mvs3atRIr732mu6//375+PiU2ScuLk69evVSVFSUmjZtqqioKPXo0UNxcXH2lgcAAK5CdgWWkydPaseOHQoPD7dpDw8P17Zt2ypdREpKSqkxe/fufcExi4qKlJeXZ7MBAICrk12BJScnR2fOnJG/v79Nu7+/v7KysipdRFZWlt1jzpgxQz4+PtYtMDCw0q8PAADMrVKLbi0Wi83nhmGUarvcY0ZFRSk3N9e6HTx48JJeHwAAmJddj+b38/OTk5NTqZmP7OzsUjMk9ggICLB7TDc3N7m5uVX6NQEAQPVh1wyLq6urQkJClJycbNOenJysTp06VbqI0NDQUmN+/vnnlzQmAAC4etj95oeTJk3SsGHD1LZtW4WGhmrBggVKT0/XmDFjJJ29VJORkaHFixdbj0lLS5MkFRQU6K+//lJaWppcXV0VHBwsSZowYYK6dOmimTNn6vbbb9dHH32kL774Qlu3bq2CUwQAANWd3YElIiJChw8f1vTp05WZmanmzZsrKSlJQUFBks4+KO78Z7K0bt3a+vGOHTu0fPlyBQUFaf/+/ZKkTp06acWKFXr66af1zDPPqEmTJkpMTFSHDh0u4dQAAMDVwu7AIknjxo3TuHHjyty3aNGiUm2GYVx0zDvvvFN33nlnZcoBAABXOd5LCAAAmB6BBQAAmB6BBQAAmB6BBQAAmB6BBQAAmB6BBQAAmB6BBQAAmF6lnsMCwDxiY2MdXYKio6MdXQKAqxwzLAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILACAS/L000/LYrHo5ZdfdnQpqCK33XabLBaLNm7c6OhSrAgsAPAP17BhQ1ksllJbzZo1FRwcrMcff1x//fVXmcceOnRIc+bMUb169TR+/HibfYcPH9Z7772n++67T8HBwfL09JSbm5saNGiggQMHas2aNVfi9Cpt9erVslgsqlGjhn766ady+50+fVp9+vSRxWJRrVq1lJaWduWKtNNLL71k829cnpiYGEnS5MmTVVxcfIWquzACCwD8gx0+fFgHDx6UJNWpU0f+/v7y9/eXr6+vTpw4oV27dmnOnDlq3bq1td+5pk2bphMnTmjKlCny9PS02RcQEKCHHnpIy5Yt065du1RcXCwXFxdlZGToo48+0qBBg9S3b18dP378ipyrvQYNGqTg4GAZhqEZM2aU22/8+PH67LPP5OzsrJUrV6pVq1ZXrkg7/Prrr4qNja1Q344dO6p3795KTU3V0qVLL3NlFUNgAYB/sB07dlg/3rRpk7KyspSVlaWcnBwdOXJEY8aMkSRlZGRo2rRpNsdmZGRo2bJlcnV11UMPPVRq7NOnT6t9+/aKj4/Xnj17dOLECRUUFGjfvn0aMWKEJGndunUaPXr0ZTzDyrNYLHrqqackSStWrNCePXtK9ZkxY4YWLFggSYqPj9dtt912RWusqOLiYo0YMUKFhYUKDQ2t0DEl//ZmudRHYAGAf7CSwOLi4qJmzZrZ7KtTp47mzp2rW265RZKUlJRks//tt9/WmTNn1LdvX9WtW7fU2Bs3btS3336rsWPH6vrrr7e2N2rUSO+88441qCxdurTM2ZuqlJeXpw8//FC7d++267ghQ4aoSZMmOnPmjGbOnGmzLyEhwRrinnrqKT388MNVVu/5iouLtWnTJh04cKBSx7/xxhv6+uuvde+99yo8PLxCx5T8u/7000/6+uuvK/W6VYnAAgD/YN99950kKTg4WK6urqX216hRQ+3atZN09vLRmTNnJEmGYWjhwoWSpHvuuafMsbt3737B1y6ZZZGk7du321/8Rfzwww+aOXOmunXrJl9fXw0ePNjuwOLk5KQnn3xSkvT+++/r0KFDkqQtW7bowQcflGEYuueee/T8889Xef2S9PPPPysqKkqNGjXSv/71L+3bt8/uMfbt26dp06bJ19dXr776aoWPc3V11eDBgyXJOovkSM6OLgAA4DglMyy33npruX1OnjwpSfLy8pKTk5MkaefOndZf3mFhYZV6bXd3d+vHJUHoUuTl5emLL75QUlKSPvvsM2VkZNjsb9Giha677jq7xx0+fLimT5+ugwcPatasWRo7dqwGDhyooqIide3aVe+9994FF7DaKzs7WwkJCVqyZInNJbs6deqUOZN1MQ8//LCOHTum+Ph41atXz65ju3TporffflufffaZ3a9b1So1wxIfH6/GjRvL3d1dISEh2rJlywX7f/XVVwoJCZG7u7uuv/56vfXWWzb7Fy1aVOYK9cLCwsqUBwCogL///tv6F3t5gcUwDKWkpEiS2rRpY23fvHmzJCkwMFABAQGVev0vv/zS+nGLFi0qNUZZsygLFy5URkaGvLy89O9//1vz58/XwYMH9cMPP1TqdVxcXDRlyhRJZy+D9enTR0eOHFGzZs20Zs2aMmem7HXixAmtWLFC/fr103XXXafIyEjt2LFD7u7uuvPOO7VmzRplZWWpZcuWdo379ttva8OGDerZs6fuv/9+u+vq0KGDpLMh6pdffrH7+Kpk9wxLYmKiIiMjFR8fr86dO2v+/Pnq06ePfv75ZzVs2LBU/3379qlv3756+OGHtXTpUn399dcaN26c6tWrZ51qkiRvb2/9+uuvNseem74BAFWr5HKQpHLvbJk/f7411AwfPtza/u2330q68MzMhRw9etR6501YWJhuvvnmCh1XUFCg9evXa926dVq3bp3++OMPm/033XST+vbtq759+6pr165VEiYkaeTIkXrhhReUlZWlffv2yd/fX0lJSapTp06lxzQMQ1999ZWWLFmiVatWKS8vT9LZy3D/+te/dO+99+rOO++Ut7d3pcbPyMjQE088IQ8PD82fP79SY9x4443y8vJSQUGBUlJS1LRp00qNUxXsDixz5szRiBEjNHLkSElSXFyc1q9fr3nz5pV529dbb72lhg0bKi4uTpLUrFkzbd++XbNmzbIJLBaLpdIpHQBgv3MDy7nB4+TJk/r999/17rvvWn92/+tf/7IJLCVBwd5LDNLZBaTDhg1TZmam3Nzc9MYbb1T42FWrVunBBx+0fu7u7q5u3bqpb9++6tevn83i3qrk4uKiG264QVlZWZKkJUuWqFGjRpUaa9euXVqyZImWLVum9PR0a3urVq103333aejQoapfv/4l1zx69Gjl5uZq5syZl/R18fX1VUFBQalweKXZFVhOnjypHTt2WBcglQgPD9e2bdvKPCYlJaXUiuTevXtr4cKFOnXqlFxcXCSdTc1BQUE6c+aMWrVqpeeee06tW7cut5aioiIVFRVZPy9JpgCAijl3fYSfn1+5/e655x7Nnz/fun5FkvVBcpVZUzFhwgStXbtW0tklBpWdpZHOrn0pLCxUYWHhZX2eyyOPPKKtW7daP9+yZYt69epl9ziJiYkaMmSI9fNGjRrpnnvu0b333qvg4OAqqVU6e+fVp59+qlatWmnSpEmXNFbdunV14MCBch8eeKXYtYYlJydHZ86ckb+/v027v7+/NXWeLysrq8z+p0+fVk5OjiSpadOmWrRokT7++GMlJCTI3d1dnTt31u+//15uLTNmzJCPj491CwwMtOdUAOAfr2SGpWbNmtYHxgUEBOiGG25QWFiYJk+erNTUVC1btkxeXl42x5asMXRzc7PrNSdPnqw333xTkvTqq6+W+fyWC7n33nu1ceNGPfHEE7rlllt06tQpffnll5oyZYpatGihwMBAjRo1SmvWrKmyP2RnzJhhXXtZ8gyTN954o1Ljnzhxwvqxh4eH7r77bg0ZMqRKw0p2drYiIyPl5OSkt99+W87Ol3Z/jYeHhyQ5fF1ppRbdnr8a2jCMC66QLqv/ue0dO3bUfffdp1tvvVVhYWH64IMPdNNNN11wmjAqKkq5ubnW7XLfww8AV5O8vDzrLb4xMTHWB8ZlZmbq999/1+bNm/XKK6+Uu7bF19dX0tmFuxU1ZcoUzZ49W5L0yiuvKDIy0u66XVxc1L17d7388svauXOn0tPT9dZbb+nf//63vLy8dOjQIb399tsaNGiQ/Pz8rH1//PFHu19LkpYtW2Z91sqzzz6rTz75RF5eXjp69Kji4+PtHq9Pnz6KjY3VjTfeqBMnTujll19Wy5Yt1aJFC7300kuVfs7KuaZOnarDhw9r1KhRatq0qQoKCmy2kru+JJXZdr4jR45I+r9/c0exK7D4+fnJycmp1GxKdnZ2qVmUEgEBAWX2d3Z2LvfkS+77v9AMi5ubm7y9vW02AEDFpKamWv94bNu2rd3Hl6xdKflldjFPPPGEXnnlFUlnn5w6efJku1+zLIGBgRo9erQ++ugjHT58WMnJyZo0aZKaNm1qnX2ZOnWqWrZsqQYNGthcBruYjRs36qGHHpJhGBo+fLhiY2Pl6+trfQLsq6++ajNjUhH+/v569tln9dtvvyklJUXjxo2Tr6+vdu7cqaioKDVu3FhhYWF66623dPjwYbvGLlGySHrevHmqVatWqe3c9aYlbSV3QZWl5N+4MuuVqpJdgcXV1VUhISFKTk62aU9OTlanTp3KPCY0NLRU/88//1xt27a1rl85n2EYSktL07XXXmtPeQCACiq5HGSxWGxuV66okksYe/fuvWjfyZMna9asWZLOhpUnnnjC7terCFdXV/Xs2VOzZ8/Wrl27tG/fPs2dO1f9+vVTzZo1lZGRUeF1GDt37tSgQYN08uRJ9erVS2+//bbN+bi7uys7O9um3V4dO3bU3LlzlZmZqTVr1mjQoEFydXXV1q1bNXbsWF177bUaMGCAVqxY4bD3W8rPz7cu3zj/SchXmt2XhCZNmqR33nlH7777rnbt2qWJEycqPT3dmjijoqJs7vUeM2aMDhw4oEmTJmnXrl169913tXDhQpt0HRsbq/Xr12vv3r1KS0vTiBEjlJaWZh0TAFC1SmYamjRpIh8fH7uP79KliyTp+++/t7kB4nyTJ0+2XgaaNWvWZQsrZWnUqJHGjRuntWvX6siRI/rss88qdPt0RkaG+vTpo9zcXN16661atWqVzR/Y/v7+1jtlX3nllQteTqkIFxcXDRw4UKtXr1ZmZqbeeustde7cWadOndLatWs1dOhQ+fv7a9iwYRW6U+fLL7+UYRjlbtHR0da+JW0ld4Odb/v27SouLpazs7M6d+58Sed5qexeiRMREaHDhw9r+vTpyszMVPPmzZWUlKSgoCBJUmZmps1tWo0bN1ZSUpImTpyouXPnqn79+nr99ddtbmk+evSoRo0apaysLPn4+Kh169bavHmz2rdvXwWnCAA4X8kMS2UuB0lS586d5ezsrJMnTyotLc36gLFzTZ061RpW5syZo4kTJ1a+4P9fUVGR8vPzK3VsSEjIRcNZXl6e+vbtq0OHDikwMFCffvppmUsOpk6dqgULFujQoUNavHixNcBcqjp16mj06NEaPXq09u7dqyVLlmjp0qXavXu3li5dqhEjRlTJLc8VVfK8nTZt2pRaeH2lVWrR7bhx47R//34VFRVpx44d1qQtnX1q7blPL5Skrl276rvvvlNRUZH27dtXaubk1Vdf1YEDB1RUVKTs7GytX7++wu8mCQCwz7Fjx6wP6gwJCanUGN7e3urXr58k6eOPPy61Pz093fouvzVq1NDMmTMVEBBQ7lZyyehiEhISVK9evUpvGzZsKHfsU6dOadCgQfrhhx/k4+OjpKSkch/l36BBA+vVhJdeeqlK3lrgfNdff72io6P1+++/a9u2bRo7duwVDw0l/7blvV/UlcSbHwLAP0xaWpqKi4slVT6wSLK+2/Ly5cutC3hLlIxf8vGff/55wa2goKDSdVSVESNGaMOGDXJxcdGHH36o5s2bX7B/VFSUnJ2dtWfPHiUmJl7W2kJDQxUfH1/pGbHK2Ldvn1JSUuTh4VGpx/pXNd78EAD+YTp37lwqYFRG79691aRJE+3Zs0dbtmyxmW1v1KhRlbzG+R544AE98MADVT6uJC1evFiLFy+ucP/rr79ep06duiy1XE4xMTGKiYm5aL8lS5ZIkoYMGXJJb0FQVZhhAQBUSo0aNfTcc89JOntZBFePY8eO6Y033pCbm5vNIl1HIrAAACptyJAhat++vdatW2ddoInq780331ROTo4ee+wx6001jsYlIQBApVksFs2fP1//+c9/rM/rQPXn6empmJiYSj2N+HIhsAAALkmrVq3KfYQ/qqdHHnnE0SWUwiUhAABgegQWAABgegQWAABgegQWAABgegQWAABgegQWAEC58vPzFRMToxYtWsjLy0s+Pj5q166dZs+efUnvUhwTEyOLxXLRbffu3VV4NqjOuK0ZAFCmAwcOqFu3btq/f78kqWbNmioqKtL27du1fft2LVu2TBs2bLikx7a7uLiobt265e53dubXFM5ihgUAUMqZM2c0YMAA7d+/X9dee62Sk5N17NgxHT9+XCtWrFCtWrWUmpqqe++995Jep1OnTsrKyip3a9SoUdWcEKo9AgsAoJRFixbpxx9/lCStXr1aPXv2lHT2/YMiIiI0f/58SdK6deu0YcMGh9WJfw4CCwCglPfff1+S1L17d4WGhpbaP2TIEDVu3FiS7HqHY6CyCCwAABvHjx/X119/LUnq06dPmX0sFotuu+02SdLnn39+xWrDPxeBBQBgY9euXSouLpYkNW/evNx+JfuysrJ05MiRSr3WTz/9pObNm8vDw0NeXl66+eab9fDDDys1NbVS4+HqRWABANj4448/rB9fd9115fY7d9+5x9gjJydHu3btst6B9Ntvv+mdd95RSEiInn766UqNiasTgQUAYCM/P9/6cc2aNcvtd+6+c4+piBtvvFEvv/yyfv31VxUWFurw4cM6duyY1q9fr5CQEBmGoRdeeEGzZ8+2/wRwVeIGdwCXXWxsrKNLUHR0tKNLwDnKuh3a1dVV4eHh6tKli7p06aL//e9/iomJ0ciRI+Xj4+OAKmEmzLAAAGzUqlXL+vHx48fL7XfuvnOPuVTu7u568cUXJUkFBQXcNg1JBBYAwHnq169v/TgjI6PcfufuO/eYqnDurdR79+6t0rFRPRFYAAA2mjVrpho1zv562LlzZ7n9SvYFBARc8PH6QFUgsAAAbNSsWVOdO3eWJH322Wdl9jEMQ+vXr5ckhYeHV3kN33zzjfXjkgfU4Z+NwAIAKGX48OGSpE2bNunbb78ttX/lypXWSzX333+/XWMbhnHB/UVFRZo2bZokydPTUz169LBrfFydCCwAgFKGDx+uFi1ayDAMDR482Lrwtbi4WCtXrtTDDz8s6eyTcMsKFDExMbJYLLJYLNZ3ey6xefNm9ezZU0uXLtWhQ4es7adOndKGDRsUFhZmDUnPPvusateufXlOEtUKtzUDAEpxdnbWxx9/rO7du2v//v3q2bOnatasqeLiYhUWFkqSWrdurWXLltk9tmEY2rBhgzUEeXh4yNPTU7m5uTp16pSks2+y+OSTT2rKlClVd1Ko1ggsAIAyNWrUSD/88INmzZqlDz/8UPv27ZOLi4tuueUWDR06VI8++qhcXV3tHrdFixaaNWuWUlJS9OOPPyonJ0dHjx5VzZo1FRwcrLCwMI0aNUotWrS4DGeF6orAAgAoV61atRQbG2v3w/9iYmIUExNT5j5fX189/vjjVVAd/klYwwIAAEyPwAIAAEyPwAIAAEyPwAIAAEyPwAIAAEyPwAIAAEyPwAIAAEyPwAIAAEyPwAIAAEyPwAIAAEyPwAIAAEyPwAIAAEyPwAIAAEyPwAIAAEyPwAIAAEzP2dEFAIBZxMbGOroERUdHO7oEwJSYYQEAAKZXqcASHx+vxo0by93dXSEhIdqyZcsF+3/11VcKCQmRu7u7rr/+er311lul+qxevVrBwcFyc3NTcHCw1qxZU5nSAADAVcjuwJKYmKjIyEhNmzZNqampCgsLU58+fZSenl5m/3379qlv374KCwtTamqqnnrqKT322GNavXq1tU9KSooiIiI0bNgwff/99xo2bJjuvvtuffvtt5U/MwAAcNWwO7DMmTNHI0aM0MiRI9WsWTPFxcUpMDBQ8+bNK7P/W2+9pYYNGyouLk7NmjXTyJEj9dBDD2nWrFnWPnFxcerVq5eioqLUtGlTRUVFqUePHoqLi6v0iQEAgKuHXYtuT548qR07dujJJ5+0aQ8PD9e2bdvKPCYlJUXh4eE2bb1799bChQt16tQpubi4KCUlRRMnTizV50KBpaioSEVFRdbPc3NzJUl5eXn2nJLdCgsLL+v4FXGxc6wONeZfoTouJE8X/16pDnVWh3/v6lCjVD3qnDFjxhWqpHxRUVGOLgFXkZLvecMwLtzRsENGRoYhyfj6669t2l944QXjpptuKvOYG2+80XjhhRds2r7++mtDkvHHH38YhmEYLi4uxrJly2z6LFu2zHB1dS23lujoaEMSGxsbGxsb21WwHTx48IIZpFK3NVssFpvPDcMo1Xax/ue32ztmVFSUJk2aZP28uLhYR44cka+v7wWPc6S8vDwFBgbq4MGD8vb2dnQ5ZaoONUrVo05qrDrVoU5qrDrVoU5qrDqGYSg/P1/169e/YD+7Aoufn5+cnJyUlZVl056dnS1/f/8yjwkICCizv7Ozs3x9fS/Yp7wxJcnNzU1ubm42bbVr167oqTiUt7e3qb95pOpRo1Q96qTGqlMd6qTGqlMd6qTGquHj43PRPnYtunV1dVVISIiSk5Nt2pOTk9WpU6cyjwkNDS3V//PPP1fbtm3l4uJywT7ljQkAAP5Z7L4kNGnSJA0bNkxt27ZVaGioFixYoPT0dI0ZM0bS2Us1GRkZWrx4sSRpzJgxevPNNzVp0iQ9/PDDSklJ0cKFC5WQkGAdc8KECerSpYtmzpyp22+/XR999JG++OILbd26tYpOEwAAVGd2B5aIiAgdPnxY06dPV2Zmppo3b66kpCQFBQVJkjIzM22eydK4cWMlJSVp4sSJmjt3rurXr6/XX39dgwcPtvbp1KmTVqxYoaefflrPPPOMmjRposTERHXo0KEKTtE83NzcFB0dXepSlplUhxql6lEnNVad6lAnNVad6lAnNV55FsO42H1EAAAAjsV7CQEAANMjsAAAANMjsAAAANMjsAAAANMjsFwBBQUFioyMVP369eXu7q5WrVppxYoVji7LRn5+vqZMmaLw8HDVq1dPFotFMTExji7LxsaNG/XQQw+padOm8vT01HXXXafbb79dO3bscHRpVmlpaerXr58aNmwoDw8P1a1bV6GhoVq6dKmjS7ugd955RxaLRV5eXo4uxerLL7+UxWIpc/vmm28cXZ6NrVu3qm/fvqpTp448PDx044036rnnnnN0WZKkBx54oNyvo9m+lqmpqRo4cKDq16+vmjVrqmnTppo+fbqOHz/u6NKs/vvf/6p3796qVauWvLy81L17d3399dcOq8een93fffedevbsKS8vL9WuXVuDBg3S3r17r2zBl4DAcgUMGjRI77//vqKjo7Vu3Tq1a9dOQ4cO1fLlyx1dmtXhw4e1YMECFRUVaeDAgY4up0zz5s3T/v37NWHCBCUlJem1115Tdna2OnbsqI0bNzq6PEnS0aNHFRgYqBdffFFJSUlavHixGjVqpGHDhun55593dHllysjI0OTJky/6WGxHefHFF5WSkmKzNW/e3NFlWS1fvlxdu3aVj4+PFi9erKSkJE2dOvXib+R2hTzzzDOlvn4pKSny8/PTddddp3bt2jm6REnSzz//rE6dOmn//v2Ki4vT2rVrNWTIEE2fPl1Dhw51dHmSpP/973/q0qWLTpw4oSVLlmjJkiUqLCxUjx49lJKS4pCaKvqz+5dfflG3bt108uRJffDBB3r33Xf122+/KSwsTH/99deVK/hSXPCdhnDJPv30U0OSsXz5cpv2Xr16GfXr1zdOnz7toMpsFRcXG8XFxYZhGMZff/1lSDKio6MdW9R5/vzzz1Jt+fn5hr+/v9GjRw8HVFRxHTp0MAIDAx1dRpn69+9vDBgwwBg+fLjh6enp6HKsNm3aZEgyVq5c6ehSynXo0CHD09PTGDt2rKNLscuXX35pSDKefvppR5diNW3aNEOSsXv3bpv2UaNGGZKMI0eOOKiy/9O7d2/D39/fOHbsmLUtLy/P8PPzMzp16uSQmir6s/uuu+4y/Pz8jNzcXGvb/v37DRcXF2PKlClXqtxLwgzLZbZmzRp5eXnprrvusml/8MEH9ccff+jbb791UGW2SqaHzeyaa64p1ebl5aXg4GAdPHjQARVVnJ+fn5ydK/Veo5fV0qVL9dVXXyk+Pt7RpVRL77zzjo4dO6apU6c6uhS7LFy4UBaLRQ899JCjS7EqeauW899Tpnbt2qpRo4ZcXV0dUZaNr7/+Wt26dVPNmjWtbbVq1VKXLl20bds2ZWZmXvGaKvKz+/Tp01q7dq0GDx5s855CQUFB6t69u9asWXO5y6wSBJbLbOfOnWrWrFmpX1YtW7a07kfl5ebm6rvvvtMtt9zi6FJsFBcX6/Tp0/rrr78UHx+v9evXm+6XWnZ2tiIjI/XSSy+pQYMGji6nXOPHj5ezs7O8vb3Vu3dvU71lx+bNm1W3bl398ssvatWqlZydnXXNNddozJgxysvLc3R5ZcrNzdWqVavUo0cPNW7c2NHlWA0fPly1a9fW2LFjtXfvXuXn52vt2rWaP3++xo8fL09PT0eXqJMnT5b51NiSth9//PFKl1Qhe/bs0YkTJ6y/d87VsmVL7d69W4WFhQ6ozD4Elsvs8OHDqlu3bqn2krbDhw9f6ZKuKuPHj9exY8c0bdo0R5diY9y4cXJxcdE111yjiRMn6vXXX9fo0aMdXZaNcePG6eabb9bYsWMdXUqZfHx8NGHCBM2fP1+bNm3Sa6+9poMHD6pbt25av369o8uTdHb9z/Hjx3XXXXcpIiJCX3zxhZ544gktXrxYffv2Nc06lnMlJCToxIkTGjFihKNLsdGoUSOlpKRo586datKkiby9vTVgwAANHz5cr732mqPLkyQFBwfrm2++UXFxsbXt9OnT1plys/48L6mrvN9FhmHo77//vtJl2c18c9RXoQtN15n9MoyZPfPMM1q2bJneeOMNhYSEOLocG0899ZRGjhyp7OxsffLJJ3rkkUd07NgxTZ482dGlSZJWr16tTz75RKmpqab9HmzdurVat25t/TwsLEx33HGHWrRooSlTpqh3794OrO6s4uJiFRYWKjo6Wk8++aQkqVu3bnJ1dVVkZKQ2bNignj17OrhKWwsXLpSvr6/uuOMOR5diY//+/RowYID8/f21atUq1atXT99++62ef/55FRQUaOHChY4uUY8++qhGjBihRx55RNOmTVNxcbFiY2N14MABSVKNGuaeA6juv4vM/dW9Cvj6+paZuo8cOSKp7MSLi4uNjdXzzz+vF154QY888oijyymlYcOGatu2rfr27at58+Zp1KhRioqKMsVq/IKCAo0fP16PPvqo6tevr6NHj+ro0aM6efKkpLN3Oh07dszBVZatdu3a6t+/v3744QedOHHC0eXI19dXkkqFpz59+kg6exupmfzwww/avn277rvvPtO9Id6TTz6pvLw8rV+/XoMHD1aXLl30xBNPKC4uTu+++66++uorR5eohx56SC+99JKWLFmiBg0aqGHDhvr555+tf4hcd911Dq6wbCXfp+X9LrJYLKpdu/YVrsp+BJbLrEWLFtq1a5dOnz5t015yrdNMt2dWF7GxsYqJiVFMTIyeeuopR5dTIe3bt9fp06dN8cyDnJwc/fnnn5o9e7bq1Klj3RISEnTs2DHVqVNH9957r6PLLFfJZRYz/EVY1poA6f9qNNtf3CWzFCNHjnRwJaWlpaUpODi41FqVktuuzbLeb+rUqcrJydGPP/6o/fv3a9u2bfr777/l6elpupneEk2aNJGHh0eZa2x+/PFH3XDDDXJ3d3dAZfYx1/+mq9Add9yhgoICrV692qb9/fffV/369dWhQwcHVVY9Pffcc4qJidHTTz+t6OhoR5dTYZs2bVKNGjV0/fXXO7oUBQQEaNOmTaW23r17y93dXZs2bTLtM2P+/vtvrV27Vq1atTLFD9jBgwdLktatW2fTnpSUJEnq2LHjFa+pPEVFRVq6dKnat29vyj+U6tevr59++kkFBQU27SXPNzHTwnA3Nzc1b95cQUFBSk9PV2Jioh5++GF5eHg4urQyOTs7a8CAAfrwww+Vn59vbU9PT9emTZs0aNAgB1ZXcaxhucz69OmjXr16aezYscrLy9MNN9yghIQEffbZZ1q6dKmcnJwcXaLVunXrdOzYMes39M8//6xVq1ZJkvr27WtzK58jzJ49W88++6xuu+029evXr9QTOs3wy2HUqFHy9vZW+/bt5e/vr5ycHK1cuVKJiYl64oknVK9ePUeXKHd3d3Xr1q1U+6JFi+Tk5FTmPke45557rJfW/Pz89Pvvv2v27Nn6888/tWjRIkeXJ0kKDw/XgAEDNH36dBUXF6tjx47avn27YmNj1b9/f/2///f/HF2i1X/+8x8dOXLElLMrkhQZGamBAweqV69emjhxovz8/PTNN99oxowZCg4Otl5mc6SdO3dq9erVatu2rdzc3PT999/rpZdecviTjSvyszs2Nlbt2rVT//799eSTT6qwsFDPPvus/Pz89Pjjjzusdrs49jEw/wz5+fnGY489ZgQEBBiurq5Gy5YtjYSEBEeXVUpQUJAhqcxt3759ji7P6Nq1a7n1meVb+d133zXCwsIMPz8/w9nZ2ahdu7bRtWtXY8mSJY4u7aLM9uC4GTNmGK1atTJ8fHwMJycno169esYdd9xh/Pe//3V0aTaOHz9uTJ061QgMDDScnZ2Nhg0bGlFRUUZhYaGjS7PRq1cvw9PT08jLy3N0KeXauHGjER4ebgQEBBgeHh7GTTfdZDz++ONGTk6Oo0szDMMwfv31V6NLly5G3bp1DVdXV+OGG24wnn76aaOgoMChdVX0Z/f27duNHj16GDVr1jS8vb2NgQMHlnpQn5lZDMOE990BAACcgzUsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9AgsAADA9P4/yzV9kfuCTfsAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X))\n",
    "x2 = list(np.arange(X,Y))\n",
    "x3 = list(np.arange(Y,n+1))\n",
    "plt.bar(x1, binom.pmf(x1, p=p, n=n), color ='gray')\n",
    "plt.bar(x2, binom.pmf(x2, p=p, n=n), color ='#DFFF00')\n",
    "plt.bar(x3, binom.pmf(x3, p=p, n=n), color ='gray')\n",
    "plt.xlim(-1,n+1)\n",
    "plt.xticks(np.arange(0,n+1), fontsize=12, ha='center')\n",
    "plt.title(f'B({n}, {p})')\n",
    "xs = np.arange(X, Y)\n",
    "prob = np.sum([binom.pmf(xs, p=p, n=n) for xs in xs])\n",
    "plt.text(7, 0.02, f'$P({np.round(X, 3)} \\leq X < {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TtKV1U-tyEBr"
   },
   "source": [
    "To find the probability between two points $(X,Y]$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "B6iatDGhyQLH",
    "outputId": "5e33d902-cdeb-47fc-8a33-ae602462fd4b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *(2, 4]* in the B(10,0.2) Distribution is:  0.2894069759999998\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "Y = 4\n",
    "n, p = [10, 0.2]\n",
    "xs = np.arange(X+1, Y+1)\n",
    "print(f'The probability between *({X}, {Y}]* in the B({n},{p}) Distribution is: ', np.sum([binom.pmf(xs, p=p, n=n) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "YlvUAe4MEXwK",
    "outputId": "495aafa0-836a-40d9-a410-7319e0eb566a"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X+1))\n",
    "x2 = list(np.arange(X+1,Y+1))\n",
    "x3 = list(np.arange(Y+1,n+1))\n",
    "plt.bar(x1, binom.pmf(x1, p=p, n=n), color ='gray')\n",
    "plt.bar(x2, binom.pmf(x2, p=p, n=n), color ='#DFFF00')\n",
    "plt.bar(x3, binom.pmf(x3, p=p, n=n), color ='gray')\n",
    "plt.xlim(-1,n+1)\n",
    "plt.xticks(np.arange(0,n+1), fontsize=12, ha='center')\n",
    "plt.title(f'B({n}, {p})')\n",
    "xs = np.arange(X+1, Y+1)\n",
    "prob = np.sum([binom.pmf(xs, p=p, n=n) for xs in xs])\n",
    "plt.text(7, 0.02, f'$P({np.round(X, 3)} < X \\leq {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dHQOxQ-gU5KC"
   },
   "source": [
    "To find the probability of a point use the code below:\n",
    "\n",
    "''\n",
    "binom.pmf($X,P,n$)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "d_KMq-YPU5KD",
    "outputId": "6cd4d50a-6beb-41c3-f0cf-eafb90385721"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of *X=2* in the B(10,0.2) Distribution is:  0.30198988800000004\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "n, p = [10, 0.2]\n",
    "print(f'The probability of *X={X}* in the B({n},{p}) Distribution is: ', binom.pmf(X, p=p, n=n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "gS2E38_2Esad",
    "outputId": "7661a644-d418-412b-da56-47312017b3a5"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X))\n",
    "x2 = X\n",
    "x3 = list(np.arange(X+1,n+1))\n",
    "plt.bar(x1, binom.pmf(x1, p=p, n=n), color ='gray')\n",
    "plt.bar(x2, binom.pmf(x2, p=p, n=n), color ='#DFFF00')\n",
    "plt.bar(x3, binom.pmf(x3, p=p, n=n), color ='gray')\n",
    "plt.xlim(-1,n+1)\n",
    "plt.xticks(np.arange(0,n+1), fontsize=12, ha='center')\n",
    "plt.title(f'B({n}, {p})')\n",
    "prob = np.sum([binom.pmf(x2, p=p, n=n)])\n",
    "plt.text(7, 0.02, f'$P({np.round(X, 3)}) = $ {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HjmA0A0fFFme"
   },
   "source": [
    "If $X_1, X_2, ..., X_n \\sim Ber(P) \\quad$ then $\\quad Y =  \\sum_{i=1}^n X_i  \\sim B(n,P)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eAUshqfZd-_d"
   },
   "source": [
    "<a name='Negative_Binomial_Distribution'></a>\n",
    "\n",
    "## **2.3. Negative Binomial (Pascal) Distribution:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EVkoQpaXe9Ri"
   },
   "source": [
    "Suppose now that $n$ independent trials, each of which results in a “success” with probability $p$ and in a “failure” with probability $1 − p$, are to be performed. If $X$ represents the number of failures before rth success, then $X$ is said to be a negative binomial random variable with parameters $(r, p)$.\n",
    "\n",
    "$P(X=i) = \\binom{r+i-1}{r-1} p^r (1-p)^{i} \\quad \\quad i = 0,1,2,...$\n",
    "\n",
    "$\\\\ $\n",
    "\n",
    "$E(X) = \\frac{r(1-p)}{p}$\n",
    "\n",
    "$Var(X) = \\frac{r(1-p)}{p^2}$\n",
    "\n",
    "$Skewness(X) = \\frac{2-p}{\\sqrt{r(1-p)}}$\n",
    "\n",
    "$Kurtosis(X) = \\frac{p^2-6p+6}{r(1-p)}$\n",
    "\n",
    "$\\\\ $\n",
    "\n",
    "Moment-generating function:\n",
    "\n",
    "$M_{x}(t) = p^r [1-(1-p)e^t]^{-r}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "HurSX6iaeUid",
    "outputId": "07b47dd4-2a49-4e64-fca9-4a6bb2720884"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "N = 10000000\n",
    "n = 15\n",
    "r, p = [4, 0.5]\n",
    "\n",
    "pas_data = nbinom.rvs(n = r, p = p, size = N)\n",
    "\n",
    "sns.histplot(pas_data, color='brown', stat='density', bins=68)\n",
    "\n",
    "plt.xlim(0,n)\n",
    "plt.xticks(list(range(0,n+1)), fontsize=12, ha='center')\n",
    "plt.title('Pascal Distribution');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "EM9m5Zim0oDM",
    "outputId": "ae3df4a6-bdc4-4fd0-842d-43eba4727385"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the NB(4,0.5) Distribution is:  4.0\n",
      "The median of the NB(4,0.5) Distribution is:  3.0\n",
      "The variance of the NB(4,0.5) Distribution is:  8.0\n",
      "The standard deviation of the NB(4,0.5) Distribution is:  2.8284\n",
      "The skewness of the NB(4,0.5) Distribution is:  1.0607\n",
      "The kurtosis of the NB(4,0.5) Distribution is:  1.625\n"
     ]
    }
   ],
   "source": [
    "r, p = [4, 0.5]\n",
    "print(f'The mean of the NB({r},{p}) Distribution is: ', np.round(nbinom.mean(p = p, n = r), 4))\n",
    "print(f'The median of the NB({r},{p}) Distribution is: ', np.round(nbinom.median(p = p, n = r), 4))\n",
    "print(f'The variance of the NB({r},{p}) Distribution is: ', np.round(nbinom.var(p = p, n = r), 4))\n",
    "print(f'The standard deviation of the NB({r},{p}) Distribution is: ', np.round(nbinom.std(p = p, n = r), 4))\n",
    "print(f'The skewness of the NB({r},{p}) Distribution is: ', np.round(nbinom.stats(p = p, n = r, moments='mvsk')[2], 4))\n",
    "print(f'The kurtosis of the NB({r},{p}) Distribution is: ', np.round(nbinom.stats(p = p, n = r, moments='mvsk')[3], 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "CBx1cK6y14kn"
   },
   "source": [
    "Integrating the PDF, gives us the cumulative distribution function (CDF) which is a function that maps values to their percentile rank in a distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "id": "X-jgGBzp14kn",
    "outputId": "0c22fcee-8f8e-48af-c1e9-83c6bf2290a5"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0, n, 0.001)\n",
    "x1 = np.arange(0, n)\n",
    "x2 = np.arange(0, n-1) + 0.999\n",
    "\n",
    "plt.scatter(x, nbinom.cdf(x, p=p, n=r), color = 'r')\n",
    "plt.scatter(x2, nbinom.cdf(x2, p=p, n=r), color = 'white', edgecolor='black', s=100)\n",
    "plt.scatter(x1, nbinom.cdf(x1, p=p, n=r), color = 'black', edgecolor='black', s=100)\n",
    "plt.xlim(0,n);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RnHxI_n92VsO"
   },
   "source": [
    "The binomial distribution histogram depends on the $n$ and $p$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 356
    },
    "id": "ZZgaR6Ob2VsQ",
    "outputId": "1c2cb41c-6030-4e79-c2a8-ce317e416468"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r1, r2, r3 = [3, 4, 7]\n",
    "p1, p2, p3 = [0.5, 0.3, 0.8]\n",
    "\n",
    "fig, axes = plt.subplots(1, 3, figsize=(15, 5), sharey=True)\n",
    "fig.suptitle('Pascal Distribution')\n",
    "\n",
    "sns.histplot(ax=axes[0], x=nbinom.rvs(n = r1, p = p1, size = N),  bins=50, color = '#A1C935')\n",
    "axes[0].set_title(f'NB({r1},{p1})')\n",
    "\n",
    "sns.histplot(ax=axes[1], x=nbinom.rvs(n = r2, p = p2, size = N),  bins=50, color = '#1AEACD')\n",
    "axes[1].set_title(f'NB({r2},{p2})')\n",
    "\n",
    "sns.histplot(ax=axes[2], x=nbinom.rvs(n = r3, p = p3, size = N),  bins=50, color = '#F75D59')\n",
    "axes[2].set_title(f'NB({r3},{p3})');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "rkcrQ1iv3GRw"
   },
   "source": [
    "To find the left probability of a point use the code below:\n",
    "\n",
    "''\n",
    "nbinom.cdf($X,P,r$)\n",
    "''\n",
    "\n",
    "To find the right probability of a point use the code below:\n",
    "\n",
    "''\n",
    "nbinom.sf($X,P,r$)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "f5Z3jo_t3GRx",
    "outputId": "fcf9d37f-17ef-47f2-df3e-ff42ef27c652"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The left probability of *4* in the NB(4,0.6) Distribution is:  0.8263295999999999\n",
      "The Right probability of *4* in the NB(4,0.6) Distribution is:  0.1736704000000001\n"
     ]
    }
   ],
   "source": [
    "X = 4\n",
    "r, p = [4, 0.6]\n",
    "print(f'The left probability of *{X}* in the NB({r},{p}) Distribution is: ', nbinom.cdf(X, p=p, n=r))\n",
    "print(f'The Right probability of *{X}* in the NB({r},{p}) Distribution is: ', nbinom.sf(X, p=p, n=r))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JbL3uCtF4H0d"
   },
   "source": [
    "To find the probability between two points $[X,Y]$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "emxN1gJN4H0e",
    "outputId": "17bbd514-d8f3-4ae7-d161-3bdb468bd3dc"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *[2, 5]* in the NB(4,0.6) Distribution is:  0.5636874239999999\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "Y = 5\n",
    "r, p = [4, 0.6]\n",
    "xs = np.arange(X, Y+1)\n",
    "print(f'The probability between *[{X}, {Y}]* in the NB({r},{p}) Distribution is: ', np.sum([nbinom.pmf(xs, p=p, n=r) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "-jQAIVGA5RHx",
    "outputId": "9a60f609-9bb0-41a1-f670-4f5f38bc5948"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X))\n",
    "x2 = list(np.arange(X,Y+1))\n",
    "x3 = list(np.arange(Y+1,n+1))\n",
    "plt.bar(x1, nbinom.pmf(x1, p=p, n=r), color ='gray')\n",
    "plt.bar(x2, nbinom.pmf(x2, p=p, n=r), color ='#DFFF00')\n",
    "plt.bar(x3, nbinom.pmf(x3, p=p, n=r), color ='gray')\n",
    "plt.xlim(-1,n+1)\n",
    "plt.xticks(np.arange(0,n+1), fontsize=12, ha='center')\n",
    "plt.title(f'NB({r}, {p})')\n",
    "xs = np.arange(X, Y+1)\n",
    "prob = np.sum([nbinom.pmf(xs, p=p, n=r) for xs in xs])\n",
    "plt.text(8, 0.02, f'$P({np.round(X, 3)} \\leq X \\leq {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tG_HoGyG5wR3"
   },
   "source": [
    "To find the probability between two points $(X,Y)$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "3Oy7TX6C5wR4",
    "outputId": "b7fb210f-6356-49cb-b484-eb4f80554a6e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *(2, 5)* in the NB(4,0.6) Distribution is:  0.2820096000000001\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "Y = 5\n",
    "r, p = [4, 0.6]\n",
    "xs = np.arange(X+1, Y)\n",
    "print(f'The probability between *({X}, {Y})* in the NB({r},{p}) Distribution is: ', np.sum([nbinom.pmf(xs, p=p, n=r) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "U-IGPmSm5wR5",
    "outputId": "e038ec9c-05ad-4f6b-fff1-a45877c54b1e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X+1))\n",
    "x2 = list(np.arange(X+1,Y))\n",
    "x3 = list(np.arange(Y,n+1))\n",
    "plt.bar(x1, nbinom.pmf(x1, p=p, n=r), color ='gray')\n",
    "plt.bar(x2, nbinom.pmf(x2, p=p, n=r), color ='#DFFF00')\n",
    "plt.bar(x3, nbinom.pmf(x3, p=p, n=r), color ='gray')\n",
    "plt.xlim(-1,n+1)\n",
    "plt.xticks(np.arange(0,n+1), fontsize=12, ha='center')\n",
    "plt.title(f'NB({r}, {p})')\n",
    "xs = np.arange(X+1, Y)\n",
    "prob = np.sum([nbinom.pmf(xs, p=p, n=r) for xs in xs])\n",
    "plt.text(8, 0.02, f'$P({np.round(X, 3)} < X < {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nDTLBWPm81nz"
   },
   "source": [
    "To find the probability between two points $[X,Y)$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "mi58xHNj81n0",
    "outputId": "fcb747ac-043c-4ab3-b856-7436fb921fff"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *[2, 5)* in the NB(4,0.6) Distribution is:  0.4893695999999999\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "Y = 5\n",
    "r, p = [4, 0.6]\n",
    "xs = np.arange(X, Y)\n",
    "print(f'The probability between *[{X}, {Y})* in the NB({r},{p}) Distribution is: ', np.sum([nbinom.pmf(xs, p=p, n=r) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "WLf_x_TF81n1",
    "outputId": "2f846f58-c9a7-41a0-d8cb-b76427a874a4"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X))\n",
    "x2 = list(np.arange(X,Y))\n",
    "x3 = list(np.arange(Y,n+1))\n",
    "plt.bar(x1, nbinom.pmf(x1, p=p, n=r), color ='gray')\n",
    "plt.bar(x2, nbinom.pmf(x2, p=p, n=r), color ='#DFFF00')\n",
    "plt.bar(x3, nbinom.pmf(x3, p=p, n=r), color ='gray')\n",
    "plt.xlim(-1,n+1)\n",
    "plt.xticks(np.arange(0,n+1), fontsize=12, ha='center')\n",
    "plt.title(f'NB({r}, {p})')\n",
    "xs = np.arange(X, Y)\n",
    "prob = np.sum([nbinom.pmf(xs, p=p, n=r) for xs in xs])\n",
    "plt.text(8, 0.02, f'$P({np.round(X, 3)} \\leq X < {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5ioDU2wm9RS-"
   },
   "source": [
    "To find the probability between two points $(X,Y]$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rLbOAAME9RS_",
    "outputId": "b6b7ef15-1a1b-4a81-90e0-4c706765c427"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *(2, 5]* in the NB(4,0.6) Distribution is:  0.3563274240000001\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "Y = 5\n",
    "r, p = [4, 0.6]\n",
    "xs = np.arange(X+1, Y+1)\n",
    "print(f'The probability between *({X}, {Y}]* in the NB({r},{p}) Distribution is: ', np.sum([nbinom.pmf(xs, p=p, n=r) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "AvNavNRm9RTA",
    "outputId": "71c92a29-780f-4ca0-cae8-2cb0e6cd69c6"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X+1))\n",
    "x2 = list(np.arange(X+1,Y+1))\n",
    "x3 = list(np.arange(Y+1,n+1))\n",
    "plt.bar(x1, nbinom.pmf(x1, p=p, n=r), color ='gray')\n",
    "plt.bar(x2, nbinom.pmf(x2, p=p, n=r), color ='#DFFF00')\n",
    "plt.bar(x3, nbinom.pmf(x3, p=p, n=r), color ='gray')\n",
    "plt.xlim(-1,n+1)\n",
    "plt.xticks(np.arange(0,n+1), fontsize=12, ha='center')\n",
    "plt.title(f'NB({r}, {p})')\n",
    "xs = np.arange(X+1, Y+1)\n",
    "prob = np.sum([nbinom.pmf(xs, p=p, n=r) for xs in xs])\n",
    "plt.text(8, 0.02, f'$P({np.round(X, 3)} < X \\leq {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "O-3lH-zz9p8f"
   },
   "source": [
    "To find the probability of a point use the code below:\n",
    "\n",
    "''\n",
    "nbinom.pmf($X,P,r$)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Nw2yekQQ9p8g",
    "outputId": "592bd653-85f5-4c61-ff66-13afe27a2d6e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of *X=2* in the NB(4,0.6) Distribution is:  0.2073599999999998\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "r, p = [4, 0.6]\n",
    "print(f'The probability of *X={X}* in the NB({r},{p}) Distribution is: ', nbinom.pmf(X, p=p, n=r))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "vi_a387B9p8h",
    "outputId": "e5ae9032-f23b-47e9-b06a-ff736ce742fd"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Jbdu2Tbt27bKuBJXr1KmTlixZotWrV2vhwoXKy8tTTEyMCgsLKxxr2rRp8vPzs27BwcHVMkcAAHDlcelEYYvFYvO9YRh2ba5KSUlR69at1bFjR5v2+Ph49e/fX23atFHPnj312WefSZIWL15c4ViJiYk6evSodTtw4EC1zBEAAFx5nDqnxt/fXx4eHnarMvn5+XarN644efKkli9frilTply0r6+vr9q0aaM9e/ZU2Mfb21ve3t5VnhcAALjyObVS4+XlpYiICKWnp9u0p6enKyYmpsqTef/991VcXKwHH3zwon2Li4u1e/duNWrUqMp1AQDA1c/pq5/Gjh2rIUOGKDIyUtHR0VqwYIGys7M1atQoSecO+eTk5GjJkiXWfbKysiRJx48f18GDB5WVlSUvLy+Fh4fbjJ2SkqJ+/fqpYcOGdnXHjRunvn37qlmzZsrPz9fUqVNVVFSkoUOHOvsUAACACTkdagYMGKDCwkJNmTJFubm5at26tdLS0hQSEiLp3M32/nrPmvbt21u/3rFjh5YuXaqQkBDt37/f2v7zzz9r06ZNWrNmjcO6v//+uwYNGqSCggIFBAQoKipKW7dutdYFAADXNothGMblnsSlUlRUJD8/Px09elT16tW73NNxyuTJk906/sSJE+3a9qt6Tv6uSKiumR89AEAVVPb3N5/9BAAATIFQAwAATIFQAwAATIFQAwAATIFQAwAATIFQAwAATIFQAwAATIFQAwAATIFQAwAATMHpj0kA3M2dd092dOdkAIA5sFIDAABMgVADAABMgVADAABMgVADAABMgVADAABMgVADAABMgVADAABMgVADAABMgVADAABMgVADAABMgVADAABMgVADAABMgVADAABMgVADAABMgVADAABMgVADAABMgVADAABMgVADAABMgVADAABMgVADAABMgVADAABMgVADAABMwaVQM2fOHIWFhcnHx0cRERHauHFjhX1zc3M1ePBg3XLLLapRo4YSEhLs+ixatEgWi8VuO336tMt1AQDAtcXpUJOamqqEhAQlJSUpMzNTsbGxio+PV3Z2tsP+xcXFCggIUFJSktq2bVvhuPXq1VNubq7N5uPj43JdAABwbXE61MycOVPDhw/XiBEj1LJlSyUnJys4OFhz58512D80NFSzZs3SQw89JD8/vwrHtVgsCgoKstmqUhcAAFxbnAo1JSUl2rFjh+Li4mza4+LitGXLlipN5Pjx4woJCVHTpk115513KjMzs8p1i4uLVVRUZLMBAABzcirUFBQU6OzZswoMDLRpDwwMVF5ensuTaNGihRYtWqRPPvlEy5Ytk4+Pjzp37qw9e/ZUqe60adPk5+dn3YKDg12eIwAAuLK5dKKwxWKx+d4wDLs2Z0RFRenBBx9U27ZtFRsbq/fff18333yz3njjjSrVTUxM1NGjR63bgQMHXJ4jAAC4snk609nf318eHh52qyP5+fl2qyhVUaNGDXXo0MG6UuNqXW9vb3l7e1fbvAAAwJXLqZUaLy8vRUREKD093aY9PT1dMTEx1TYpwzCUlZWlRo0aXdK6AADg6uXUSo0kjR07VkOGDFFkZKSio6O1YMECZWdna9SoUZLOHfLJycnRkiVLrPtkZWVJOncy8MGDB5WVlSUvLy+Fh4dLkiZPnqyoqCjddNNNKioq0uuvv66srCzNnj270nUBAMC1zelQM2DAABUWFmrKlCnKzc1V69atlZaWppCQEEnnbrb313vHtG/f3vr1jh07tHTpUoWEhGj//v2SpCNHjuiRRx5RXl6e/Pz81L59e3311Vfq2LFjpesCAIBrm8UwDONyT+JSKSoqkp+fn44ePap69epd7uk4ZfLkyW4df+LEiXZt++X6yd+VESrHP3rufK6OnicA4MpW2d/ffPYTAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBUINAAAwBc/LPYGr0eTJk9029sSJE902NgAAZsZKDQAAMAVCDQAAMAVCDQAAMAWXQs2cOXMUFhYmHx8fRUREaOPGjRX2zc3N1eDBg3XLLbeoRo0aSkhIsOuzcOFCxcbGqn79+qpfv7569uypbdu22fSZNGmSLBaLzRYUFOTK9AEAgAk5HWpSU1OVkJCgpKQkZWZmKjY2VvHx8crOznbYv7i4WAEBAUpKSlLbtm0d9lm/fr0GDRqkdevWKSMjQ82aNVNcXJxycnJs+rVq1Uq5ubnWbefOnc5OHwAAmJTToWbmzJkaPny4RowYoZYtWyo5OVnBwcGaO3euw/6hoaGaNWuWHnroIfn5+Tns895772n06NFq166dWrRooYULF6qsrExffPGFTT9PT08FBQVZt4CAAGenDwAATMqpUFNSUqIdO3YoLi7Opj0uLk5btmyptkmdPHlSZ86cUYMGDWza9+zZo8aNGyssLEwDBw7U3r17LzhOcXGxioqKbDYAAGBOToWagoICnT17VoGBgTbtgYGBysvLq7ZJjR8/Xk2aNFHPnj2tbZ06ddKSJUu0evVqLVy4UHl5eYqJiVFhYWGF40ybNk1+fn7WLTg4uNrmCAAAriwunShssVhsvjcMw67NVa+88oqWLVumjz76SD4+Ptb2+Ph49e/fX23atFHPnj312WefSZIWL15c4ViJiYk6evSodTtw4EC1zBEAAFx5nLqjsL+/vzw8POxWZfLz8+1Wb1wxY8YMvfTSS1q7dq1uvfXWC/b19fVVmzZttGfPngr7eHt7y9vbu8rzAgAAVz6nVmq8vLwUERGh9PR0m/b09HTFxMRUaSLTp0/XCy+8oM8//1yRkZEX7V9cXKzdu3erUaNGVaoLAADMwenPfho7dqyGDBmiyMhIRUdHa8GCBcrOztaoUaMknTvkk5OToyVLllj3ycrKkiQdP35cBw8eVFZWlry8vBQeHi7p3CGnCRMmaOnSpQoNDbWuBNWpU0d16tSRJI0bN059+/ZVs2bNlJ+fr6lTp6qoqEhDhw6t0gsAAADMwelQM2DAABUWFmrKlCnKzc1V69atlZaWppCQEEnnbrb313vWtG/f3vr1jh07tHTpUoWEhGj//v2Szt3Mr6SkRPfee6/NfhMnTtSkSZMkSb///rsGDRqkgoICBQQEKCoqSlu3brXWBQAA1zaXPqV79OjRGj16tMPHFi1aZNdmGMYFxysPNxeyfPnyykwNAABco/jsJwAAYAqEGgAAYAqEGgAAYAqEGgAAYAqEGgAAYAqEGgAAYAqEGgAAYAqEGgAAYAou3XwPMJvJkye7beyJEye6bWwAwP+HlRoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKhBoAAGAKLoWaOXPmKCwsTD4+PoqIiNDGjRsr7Jubm6vBgwfrlltuUY0aNZSQkOCw34oVKxQeHi5vb2+Fh4dr5cqVVaoLAACuLU6HmtTUVCUkJCgpKUmZmZmKjY1VfHy8srOzHfYvLi5WQECAkpKS1LZtW4d9MjIyNGDAAA0ZMkTfffedhgwZovvvv19ff/21y3UBAMC1xelQM3PmTA0fPlwjRoxQy5YtlZycrODgYM2dO9dh/9DQUM2aNUsPPfSQ/Pz8HPZJTk5Wr169lJiYqBYtWigxMVE9evRQcnKyy3UBAMC1xalQU1JSoh07diguLs6mPS4uTlu2bHF5EhkZGXZj9u7d2zqmq3WLi4tVVFRkswEAAHNyKtQUFBTo7NmzCgwMtGkPDAxUXl6ey5PIy8u74Jiu1p02bZr8/PysW3BwsMtzBAAAVzaXThS2WCw23xuGYdfmjjGdrZuYmKijR49atwMHDlRpjgAA4Mrl6Uxnf39/eXh42K2O5Ofn262iOCMoKOiCY7pa19vbW97e3i7PCwAAXD2cWqnx8vJSRESE0tPTbdrT09MVExPj8iSio6PtxlyzZo11THfVBQAA5uHUSo0kjR07VkOGDFFkZKSio6O1YMECZWdna9SoUZLOHfLJycnRkiVLrPtkZWVJko4fP66DBw8qKytLXl5eCg8PlyQ9+eST6tKli15++WXddddd+vjjj7V27Vpt2rSp0nUBAMC1zelQM2DAABUWFmrKlCnKzc1V69atlZaWppCQEEnnbrb313vHtG/f3vr1jh07tHTpUoWEhGj//v2SpJiYGC1fvlzPP/+8JkyYoObNmys1NVWdOnWqdF0AAHBtczrUSNLo0aM1evRoh48tWrTIrs0wjIuOee+99+ree+91uS4AALi28dlPAADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFAg1AADAFFwKNXPmzFFYWJh8fHwUERGhjRs3XrD/hg0bFBERIR8fH91www2aN2+ezePdunWTxWKx2+644w5rn0mTJtk9HhQU5Mr0AQCACTkdalJTU5WQkKCkpCRlZmYqNjZW8fHxys7Odth/37596tOnj2JjY5WZmannnntOTzzxhFasWGHt89FHHyk3N9e67dq1Sx4eHrrvvvtsxmrVqpVNv507dzo7fQAAYFKezu4wc+ZMDR8+XCNGjJAkJScna/Xq1Zo7d66mTZtm13/evHlq1qyZkpOTJUktW7bU9u3bNWPGDPXv31+S1KBBA5t9li9frtq1a9uFGk9PT1ZnAACAQ06t1JSUlGjHjh2Ki4uzaY+Li9OWLVsc7pORkWHXv3fv3tq+fbvOnDnjcJ+UlBQNHDhQvr6+Nu179uxR48aNFRYWpoEDB2rv3r0XnG9xcbGKiopsNgAAYE5OhZqCggKdPXtWgYGBNu2BgYHKy8tzuE9eXp7D/qWlpSooKLDrv23bNu3atcu6ElSuU6dOWrJkiVavXq2FCxcqLy9PMTExKiwsrHC+06ZNk5+fn3ULDg6u7FMFAABXGacPP0mSxWKx+d4wDLu2i/V31C6dW6Vp3bq1OnbsaNMeHx9v/bpNmzaKjo5W8+bNtXjxYo0dO9Zh3cTERJvHioqKCDa4YkyePNltY0+cONFtYwPAlcqpUOPv7y8PDw+7VZn8/Hy71ZhyQUFBDvt7enqqYcOGNu0nT57U8uXLNWXKlIvOxdfXV23atNGePXsq7OPt7S1vb++LjgUAAK5+Th1+8vLyUkREhNLT023a09PTFRMT43Cf6Ohou/5r1qxRZGSkatasadP+/vvvq7i4WA8++OBF51JcXKzdu3erUaNGzjwFAABgUk5f0j127Fi99dZbevvtt7V792499dRTys7O1qhRoySdO+Tz0EMPWfuPGjVKv/32m8aOHavdu3fr7bffVkpKisaNG2c3dkpKivr162e3giNJ48aN04YNG7Rv3z59/fXXuvfee1VUVKShQ4c6+xQAAIAJOX1OzYABA1RYWKgpU6YoNzdXrVu3VlpamkJCQiRJubm5NvesCQsLU1pamp566inNnj1bjRs31uuvv269nLvczz//rE2bNmnNmjUO6/7+++8aNGiQCgoKFBAQoKioKG3dutVaFwAAXNtcOlF49OjRGj16tMPHFi1aZNfWtWtXffvttxcc8+abb7aeQOzI8uXLnZojAAC4tvDZTwAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBRcCjVz5sxRWFiYfHx8FBERoY0bN16w/4YNGxQRESEfHx/dcMMNmjdvns3jixYtksVisdtOnz5dpboAAODa4XSoSU1NVUJCgpKSkpSZmanY2FjFx8crOzvbYf99+/apT58+io2NVWZmpp577jk98cQTWrFihU2/evXqKTc312bz8fFxuS4AALi2OB1qZs6cqeHDh2vEiBFq2bKlkpOTFRwcrLlz5zrsP2/ePDVr1kzJyclq2bKlRowYoWHDhmnGjBk2/SwWi4KCgmy2qtSVpOLiYhUVFdlsAADAnJwKNSUlJdqxY4fi4uJs2uPi4rRlyxaH+2RkZNj17927t7Zv364zZ85Y244fP66QkBA1bdpUd955pzIzM6tUV5KmTZsmPz8/6xYcHFzp5woAAK4uToWagoICnT17VoGBgTbtgYGBysvLc7hPXl6ew/6lpaUqKCiQJLVo0UKLFi3SJ598omXLlsnHx0edO3fWnj17XK4rSYmJiTp69Kh1O3DggDNPFwAAXEU8XdnJYrHYfG8Yhl3bxfqf3x4VFaWoqCjr4507d9Ztt92mN954Q6+//rrLdb29veXt7X2RZwMAAMzAqZUaf39/eXh42K2O5Ofn262ilAsKCnLY39PTUw0bNnQ8qRo11KFDB+tKjSt1AQDAtcWpUOPl5aWIiAilp6fbtKenpysmJsbhPtHR0Xb916xZo8jISNWsWdPhPoZhKCsrS40aNXK5LgAAuLY4ffhp7NixGjJkiCIjIxUdHa0FCxYoOztbo0aNknTuPJacnBwtWbJEkjRq1Ci9+eabGjt2rEaOHKmMjAylpKRo2bJl1jEnT56sqKgo3XTTTSoqKtLrr7+urKwszZ49u9J1AQDAtc3pUDNgwAAVFhZqypQpys3NVevWrZWWlqaQkBBJUm5urs29Y8LCwpSWlqannnpKs2fPVuPGjfX666+rf//+1j5HjhzRI488ory8PPn5+al9+/b66quv1LFjx0rXBQAA1zaXThQePXq0Ro8e7fCxRYsW2bV17dpV3377bYXjvfbaa3rttdeqVBcAAFzb+OwnAABgCoQaAABgCi4dfgJwdZo8ebJbx584caJbxweAC2GlBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgAAmAKhBgDc4Pnnn5fFYtErr7xSrePefvvtslgs+vLLL6t1XMAMCDUA4ECzZs1ksVjsttq1ays8PFz/+te/dPDgQYf7/v7775o5c6YCAgI0ZswYm8cKCwv1P//zP3rwwQcVHh4uX19feXt7q2nTpurXr59Wrlx5wXlNmjRJkjRu3DiVlZVVy3O9XI4dO6ZJkyapTZs2qlOnjvz8/NShQwe9+uqrKikpcXq8qr62J0+e1KpVqzR16lTdc889CgkJsf67l7/uuLJ5Xu4JAMCVprCwUAcOHJAk1a9fX15eXpKk0tJSFRYWavfu3dq9e7dSU1OVkZGh4OBgm/2TkpJ06tQpTZkyRb6+vjaPBQUFqbS01Pq9j4+PatasqZycHOXk5Ojjjz9WfHy8PvzwQ9WuXdtublFRUerdu7dWr16td999Vw899FB1P/1L4rffflO3bt20f/9+SVLt2rVVXFys7du3a/v27Xrvvff0xRdfqH79+pUes6qv7bZt29SnT58qPzdcPqzUAMBf7Nixw/r1unXrlJeXp7y8PBUUFOjQoUMaNWqUJCknJ0dJSUk2++bk5Oi9996Tl5eXhg0bZjd2aWmpOnbsqDlz5ujXX3/VqVOndPz4ce3bt0/Dhw+XJK1atUr//Oc/K5xfef3qPrR1qZw9e1Z9+/bV/v371ahRI6Wnp+vEiRM6efKkli9frrp16yozM1MPPPCAU+NWx2tbv3599ejRQ08//bSWLVumoKCgKj1XXFqEGgD4i/JQU7NmTbVs2dLmsfr162v27Nlq1aqVJCktLc3m8YULF+rs2bPq06ePGjRoYDf2l19+qa+//lqPPvqobrjhBmt7aGio3nrrLesv3Hfffde6WvRX5WN///332rx5s+tP9DJZtGiRdu7cKUlasWKFevbsKUmqUaOGBgwYoPnz50s6F0C++OKLSo9b1dc2NjZWhw4d0tq1a/XKK69o4MCB8vb2dvl54tIj1ADAX3z77beSpPDwcOuhp/PVqFFDHTp0kHTuUNXZs2clSYZhKCUlRZI0ePBgh2N37979grXLVxQkafv27Q77eHl5qX///pKkBQsWXHC8K9HixYslnXstoqOj7R4fOHCgwsLCJElLliyp9LhVfW09PDwqXQtXJpdCzZw5cxQWFiYfHx9FRERo48aNF+y/YcMGRUREyMfHRzfccIPmzZtn8/jChQsVGxur+vXrq379+urZs6e2bdtm02fSpEl2J+yxLAjAHcpXatq2bVthn/ITWevUqWP9Zbhr1y79/vvvks791e8KHx8f69flYcmRLl26SJI+//xzl+pcLidPnrSuLsXHxzvsY7FYdPvtt0uS1qxZU221K/va4urldKhJTU1VQkKCkpKSlJmZqdjYWMXHxys7O9th/3379qlPnz6KjY1VZmamnnvuOT3xxBNasWKFtc/69es1aNAgrVu3ThkZGWrWrJni4uKUk5NjM1arVq2Um5tr3cqXLwGguhw+fFj79u2TVHGoMQxDGRkZkqTbbrvN2v7VV19JkoKDg13+o2v9+vXWr9u0aVNhv06dOkmS8vPz9eOPP7pU63LYvXu39aqt1q1bV9iv/LG8vDwdOnSoWmpX9rXF1cvpUDNz5kwNHz5cI0aMUMuWLZWcnKzg4GDNnTvXYf958+apWbNmSk5OVsuWLTVixAgNGzZMM2bMsPZ57733NHr0aLVr104tWrTQwoULVVZWZncs1dPTU0FBQdYtICDA2ekDwAWVH3qSpHbt2jnsM3/+fGvwGTp0qLX966+/lnThFZ4LOXLkiKZNmybp3ErPLbfcUmHfm266SXXq1JEka8C6mEWLFjm8TL2y2/mhwFV//PGH9esmTZpU2O/8x87fx1XOvLa4ejl1SXdJSYl27Nih8ePH27THxcVpy5YtDvfJyMhQXFycTVvv3r2VkpKiM2fOqGbNmnb7nDx5UmfOnLE7yW7Pnj1q3LixvL291alTJ7300ks2J4P9VXFxsYqLi63fFxUVXfQ5AqhekydPduv4EydOrNbxzg8154eTkpIS7dmzR2+//baSk5MlSX//+99tQk35L19X/uAqKyvTkCFDlJubK29vb73xxhsX3adhw4Y6fvx4pX/p16pVS4GBgU7PrZyj84ucdezYMevXji6rdvTY+fu4wpXXFlcnp0JNQUGBzp49a/efIjAwUHl5eQ73ycvLc9i/tLRUBQUFatSokd0+48ePV5MmTaxnxEvnllqXLFmim2++WX/++aemTp2qmJgYff/992rYsKHD2tOmTXP7GyoAczn/cm5/f/8K+w0ePFjz58+3Obm0/GZ8jq56upgnn3xSn376qaRz5y1WZrWnQYMG+u233yq8CeBfDRgwQAMGDHB6blc7V15bXJ1cuvmexWKx+d4wDLu2i/V31C6du+/CsmXLtH79epuTus4/oaxNmzaKjo5W8+bNtXjxYo0dO9Zh3cTERJvHioqK7G6SBQDnK1+pqV27turWrSvp3HtVnTp11KhRI3Xq1EkPPPCAw0NTp0+fliSnLwMeN26c3nzzTUnSa6+95vD+No7UqlXLpu7VoPw1lc6tylfk/MfO38dZrr62uDo5FWr8/f3l4eFhtyqTn59f4ZJmUFCQw/6enp52KywzZszQSy+9pLVr1+rWW2+94Fx8fX3Vpk0b7dmzp8I+3t7e3GMAQKUVFRXpl19+kXTuisunn37aqf3L39MOHz5c6X2eeeYZvfrqq5Kk6dOnKyEhodL7lp9AW9Fq9ZWocePG1q9zcnIqfK8//0KR8/dxRlVeW1ydnDpR2MvLSxEREUpPT7dpT09PV0xMjMN9oqOj7fqvWbNGkZGRNufTTJ8+XS+88II+//xzRUZGXnQuxcXF2r17t8PDVwDgiszMTOtKcmXeh/6q/Fyayl6t8/TTT2v69OmSzq1Sjxs3zql65XUqew5PamqqzcUWzm4VnTvpjJYtW6pGjXO/enbt2lVhv/LHgoKCXDqcV9XXFlcnpw8/jR07VkOGDFFkZKSio6O1YMECZWdnW2/bnZiYqJycHOsNk0aNGqU333xTY8eO1ciRI5WRkaGUlBQtW7bMOuYrr7yiCRMmaOnSpQoNDbWu7NSpU8d6dv+4cePUt29fNWvWTPn5+Zo6daqKiopsTtIDgKooP/RksVhsLtWurPDwcH3yySfau3fvRfuOGzfOuorwyiuvOL0qdOzYMRUUFEiS3V2PK3Lq1Cn9+eefTtU5nysfMvlXtWvXVufOnbVx40Z9/vnnDp+3YRhavXq1JNldaFIZVX1tcfVy+pLuAQMGKDk5WVOmTFG7du301VdfKS0tTSEhIZKk3Nxcm3vWhIWFKS0tTevXr1e7du30wgsv6PXXX7feDVM6d+JWSUmJ7r33XjVq1Mi6nX/Z9++//65Bgwbplltu0T333CMvLy9t3brVWhcAqqr8JOHmzZvLz8/P6f3Lb4j33Xff2Vx5+Vfn/9KdMWOGS790t2/frrKyMnl6eqpz586V2ufhhx+WYRgub926dXN6no6U/zG6bt0662Xw5/vggw+swdDZD+ysjtcWVy+XThQePXq0Ro8e7fCxRYsW2bV17drV5jLJvyr/lNYLWb58eWWnBwAuKX+fcuXQkyR17txZnp6eKikpUVZWlvUGeed79tlnrb90Z86cqaeeesqlWuVh4LbbbrOuaF8thg4dqlmzZmnnzp3q37+/Fi9erB49eqisrEwrVqzQyJEjJZ27QKRHjx52+y9atEj/+Mc/JJ0LRuVhqzpe28OHD9vcbbj8RoEnT560roxJ5+5OfLW97tcCPvsJACSdOHFCP/30kyQpIiLCpTHq1aunO+64Q5L0ySef2D2enZ1t/WTtGjVq6OWXX77gOSznr1b/Vfn4FX3G1JXM09NTn3zyiUJDQ5WTk6OePXvK19dXvr6+uv/++1VUVKT27dvrvffeq/SY1fXatm/fXgEBAdat/IMvp0+fbtP+2GOPVf2FQLVzaaUGAMwmKyvL+le5q6FGkv75z3/q448/1tKlSzV16lSbW1eUj1/+9cXObzl+/LjD9n379ikjI0O1atVy+vDMlSI0NFT//e9/NWPGDH300Ufat2+fatasqVatWmnQoEF6/PHHnbrZX3W9tri6EWoAQOcOHZVf+VQVvXv3VvPmzfXrr79q48aN1vNspHO/yKujxjvvvCPp3KdZ169fv8rjXS5169bV5MmTnb5J6sMPP6yHH37Ypq26XtvKnA6BKxeHnwCgGtWoUUMvvPCCJOk///lPtY9/4sQJvfHGG/L29q72j4gArnaEGgCoZgMHDlTHjh21atUqh1f3VMWbb76pgoICPfHEE1z9CfwFh58AoJpZLBbNnz9f//u//2tzxUx18PX11aRJk7g7LuAAoQYA3KBdu3YOPx+qqrjqBqgYh58AAIApEGoAAIApEGoAAIApEGoAAIApcKIwAFNy9oZuzuD+MMCViZUaAABgCoQaAABgCoQaAABgCoQaAABgCoQaAABgCoQaAABgCoQaAABgCoQaAABgCoQaAABgCoQaAABgCoQaAABgCnz2EwBUEz5vCri8WKkBAACmQKgBAACmQKgBAACmQKgBAACmQKgBAACmwNVPAHAV44or4P/DSg0AADAFl0LNnDlzFBYWJh8fH0VERGjjxo0X7L9hwwZFRETIx8dHN9xwg+bNm2fXZ8WKFQoPD5e3t7fCw8O1cuXKKtcFAADXDqcPP6WmpiohIUFz5sxR586dNX/+fMXHx+uHH35Qs2bN7Prv27dPffr00ciRI/Xuu+9q8+bNGj16tAICAtS/f39JUkZGhgYMGKAXXnhBd999t1auXKn7779fmzZtUqdOnVyqCwBwDw554Url9ErNzJkzNXz4cI0YMUItW7ZUcnKygoODNXfuXIf9582bp2bNmik5OVktW7bUiBEjNGzYMM2YMcPaJzk5Wb169VJiYqJatGihxMRE9ejRQ8nJyS7XBQAA1xanVmpKSkq0Y8cOjR8/3qY9Li5OW7ZscbhPRkaG4uLibNp69+6tlJQUnTlzRjVr1lRGRoaeeuopuz7locaVupJUXFys4uJi6/dHjx6VJBUVFV34iV7E6dOnq7T/hVQ0N3fWrKjuMbdWlIp06Z/r5Xh9r5WaFdW9HDXdXZeal77mtGnT3FZTkhITE6+ImnCs/OfCMIwLdzSckJOTY0gyNm/ebNP+4osvGjfffLPDfW666SbjxRdftGnbvHmzIcn4448/DMMwjJo1axrvvfeeTZ/33nvP8PLycrmuYRjGxIkTDUlsbGxsbGxsJtgOHDhwwZzi0iXdFovF5nvDMOzaLtb/r+2VGdPZuomJiRo7dqz1+7KyMh06dEgNGza84H7VqaioSMHBwTpw4IDq1atHTWpeNXWpaa6al6suNalZHQzD0LFjx9S4ceML9nMq1Pj7+8vDw0N5eXk27fn5+QoMDHS4T1BQkMP+np6eatiw4QX7lI/pSl1J8vb2lre3t03bddddV/ETdKN69epd0h8Aapqv5uWqS01z1bxcdalJzary8/O7aB+nThT28vJSRESE0tPTbdrT09MVExPjcJ/o6Gi7/mvWrFFkZKRq1qx5wT7lY7pSFwAAXFucPvw0duxYDRkyRJGRkYqOjtaCBQuUnZ2tUaNGSTp3yCcnJ0dLliyRJI0aNUpvvvmmxo4dq5EjRyojI0MpKSlatmyZdcwnn3xSXbp00csvv6y77rpLH3/8sdauXatNmzZVui4AALjGXfCMmwrMnj3bCAkJMby8vIzbbrvN2LBhg/WxoUOHGl27drXpv379eqN9+/aGl5eXERoaasydO9duzA8++MC45ZZbjJo1axotWrQwVqxY4VTdK9Xp06eNiRMnGqdPn6YmNa+qutQ0V83LVZea1LyULIZxseujAAAArnx89hMAADAFQg0AADAFQg0AADAFQg0AADAFQo2bHD9+XAkJCWrcuLF8fHzUrl07LV++3K01jx07pmeeeUZxcXEKCAiQxWLRpEmT3Fbvyy+/1LBhw9SiRQv5+vqqSZMmuuuuu7Rjxw631czKytIdd9yhZs2aqVatWmrQoIGio6P17rvvuq2mI2+99ZYsFovq1Knjthrr16+XxWJxuG3dutVtdSVp06ZN6tOnj+rXr69atWrppptu0gsvvOCWWg8//HCFz9OdzzUzM1P9+vVT48aNVbt2bbVo0UJTpkzRyZMn3VJPkrZt26bevXurbt26qlOnjrp3767NmzdX2/jOvAd8++236tmzp+rUqaPrrrtO99xzj/bu3eu2mps2bdKIESMUEREhb29vWSwW7d+/3+l6la159uxZzZw5U7fffruaNm2q2rVrq2XLlho/fryOHDnituf5+uuvKyoqSv7+/vL29lazZs00cOBAff/9926reT7DMNSlSxdZLBY99thjTtd0pm5F/3dbtGjhUt3qQKhxk3vuuUeLFy/WxIkTtWrVKnXo0EGDBg3S0qVL3VazsLBQCxYsUHFxsfr16+e2OuXmzp2r/fv368knn1RaWppmzZql/Px8RUVF6csvv3RLzSNHjig4OFgvvfSS0tLStGTJEoWGhmrIkCGaOnWqW2r+VU5OjsaNG3fR23VXl5deekkZGRk2W+vWrd1Wb+nSperatav8/Py0ZMkSpaWl6dlnn734B8m5aMKECXbPLyMjQ/7+/mrSpIk6dOhQ7TV/+OEHxcTEaP/+/UpOTtann36qgQMHasqUKRo0aFC115Okb775Rl26dNGpU6f0zjvv6J133tHp06fVo0cPZWRkVEuNyr4H/Pjjj+rWrZtKSkr0/vvv6+2339bPP/+s2NhYHTx40C01v/jiC61du1bNmjWr8k1TK1Pz1KlTmjRpkkJCQpScnKy0tDSNHDlSCxYsUOfOnXXq1Klqr1neLz4+Xm+99ZbWrFmjyZMnKzMzU506ddJPP/3klprnmz17tn755Ren6lSlbq1atez+76amplapfpVc3ivKzemzzz4zJBlLly61ae/Vq5fRuHFjo7S01C11y8rKjLKyMsMwDOPgwYOGJGPixIluqWUYhvHnn3/atR07dswIDAw0evTo4ba6jnTq1MkIDg6+JLXuvPNOo2/fvsbQoUMNX19ft9VZt26dIcn44IMP3Fbjr37//XfD19fXePTRRy9ZTUfWr19vSDKef/55t4yflJRkSDJ++eUXm/ZHHnnEkGQcOnSo2mv27t3bCAwMNE6cOGFtKyoqMvz9/Y2YmJhqqVHZ94D77rvP8Pf3N44ePWpt279/v1GzZk3jmWeecUvNs2fPWr+ePn26IcnYt2+fU7WcqVlaWmoUFBTY7fvBBx8Ykox33nmn2mtW5IcffjAkGRMmTHBrzX379hl16tQxPvroI0OSMWbMGKfqOVvX3e+BrmClxg1WrlypOnXq6L777rNp/8c//qE//vhDX3/9tVvqli/9XSrXX3+9XVudOnUUHh6uAwcOXLJ5SOc+H8zT06XPZ3XKu+++qw0bNmjOnDlur3U5vPXWWzpx4oSeffbZyzqPlJQUWSwWDRs2zC3jl39Ey18/S+a6665TjRo15OXlVe01N2/erG7duql27drWtrp166pLly7asmWLcnNzq1yjMu8BpaWl+vTTT9W/f3+bz+4JCQlR9+7dtXLlymqvKUk1alTfr5vK1PTw8LB+vuD5OnbsKElOv0dV5f01ICBAkpx+j3K25iOPPKJevXrp7rvvdqpOVeteSQg1brBr1y61bNnS7gf41ltvtT5uVkePHtW3336rVq1aubVOWVmZSktLdfDgQc2ZM0erV692+y/i/Px8JSQk6D//+Y+aNm3q1lrnGzNmjDw9PVWvXj317t3b5uNDqttXX32lBg0a6Mcff1S7du3k6emp66+/XqNGjVJRUZHb6p7v6NGj+vDDD9WjRw+FhYW5pcbQoUN13XXX6dFHH9XevXt17Ngxffrpp5o/f77GjBkjX1/faq9ZUlJi9wG7kqxtO3furPaajvz66686deqU9f3ofLfeeqt++eUXnT59+pLM5XIoPzTu7veos2fPqri4WD/++KNGjBih66+/Xv/4xz/cVu+tt97Stm3b9Oabb7qthiOnTp1SUFCQPDw81LRpUz322GM6dOjQJZ3D+dz/p+01qLCwUDfccINde4MGDayPm9WYMWN04sQJJSUlubXO6NGjNX/+fEnnPvD09ddf1z//+U+317zlllv06KOPurVOOT8/Pz355JPq1q2bGjZsqF9++UXTp09Xt27d9Nlnn6l3797VXjMnJ0cnT57Ufffdp8TERCUnJ+ubb77RxIkTtWvXLm3cuNHtf8EtW7ZMp06d0vDhw91WIzQ0VBkZGbr77rvVvHlza/sTTzyh5ORkt9QMDw/X1q1bVVZWZl21KC0tta7cXqr3hfI65e9H52vQoIEMw9Dhw4fVqFGjSzKfSyknJ0fjx49XZGSk7rzzTrfW8vX1VXFxsSTp5ptv1vr16xUcHOyWWuXn+b3yyiuX7Fw/SWrbtq3atm1rPcdvw4YNeu211/TFF1/om2++ceuFFBUh1LjJhd74r9ZlvYuZMGGC3nvvPb3xxhuKiIhwa63nnntOI0aMUH5+vv7v//5Pjz32mE6cOKFx48a5pd6KFSv0f//3f8rMzLxk/37t27dX+/btrd/Hxsbq7rvvVps2bfTMM8+4JdSUlZXp9OnTmjhxosaPHy9J6tatm7y8vJSQkKAvvvhCPXv2rPa650tJSVHDhg2rvIR+Ifv371ffvn0VGBioDz/8UAEBAfr66681depUHT9+XCkpKdVe8/HHH9fw4cP12GOPKSkpSWVlZZo8ebJ+++03SdV7eKYyrrX3qEOHDqlPnz4yDEOpqaluf723bNmikpIS/frrr3rttdfUvXt3ffHFF25ZIRo1apTatm2rkSNHVvvYF/LUU0/ZfN+rVy+1b99e9957rxYuXGj3+KXA4Sc3aNiwocO/usqX5Bz9hXS1mzx5sqZOnaoXX3zR5csIndGsWTNFRkaqT58+mjt3rh555BElJiY6feVGZRw/flxjxozR448/rsaNG+vIkSM6cuSISkpKJJ27IuvEiRPVXteR6667Tnfeeaf++9//On31RmWUn4Pw18AUHx8v6dxlwO703//+V9u3b9eDDz7o8FBNdRk/fryKioq0evVq9e/fX126dNHTTz+t5ORkvf3229qwYUO11xw2bJj+85//6J133lHTpk3VrFkz/fDDD9Yg3qRJk2qv6Uj5v3FF71EWi0XXXXfdJZnLpXL48GH16tVLOTk5Sk9Pd7iSXt1uu+02RUVF6YEHHtC6detkGIaee+65aq/z4Ycf6vPPP9crr7yio0ePWt+fpHOHPI8cOaIzZ85Ue92K3H333fL19XX7bScqQqhxgzZt2mj37t0qLS21aS8/Zu7Oy3Evh8mTJ2vSpEmaNGmSW/7TVkbHjh1VWlrq0n02LqagoEB//vmnXn31VdWvX9+6LVu2TCdOnFD9+vX1wAMPVHvdihj//0ur3fHXtKPzLM6v6e6/bstXSEaMGOHWOllZWQoPD7c7d6b88nF3nff27LPPqqCgQDt37tT+/fu1ZcsWHT58WL6+vm5f3SzXvHlz1apVy+E5PDt37tSNN94oHx+fSzKXS+Hw4cPq2bOn9u3bp/T09Ap/xt2pbt26atGihX7++edqH3vXrl0qLS1VVFSUzfuTJC1cuFD169fXZ599Vu11L8QwjEu+8liOUOMGd999t44fP64VK1bYtC9evFiNGzdWp06dLtPMqt8LL7ygSZMm6fnnn9fEiRMv2zzWrVunGjVquOUvsKCgIK1bt85u6927t3x8fLRu3bpLdo+cw4cP69NPP1W7du3c8ounf//+kqRVq1bZtKelpUmSoqKiqr1mueLiYr377rvq2LGj24N/48aN9f333+v48eM27eX3i3HnieDe3t5q3bq1QkJClJ2drdTUVI0cOVK1atVyW83zeXp6qm/fvvroo4907Ngxa3t2drbWrVune+6555LM41IoDzR79+7VmjVrbA7nXkrlQfbGG2+s9rEffvhhh+9PktSvXz+tW7dOf/vb36q9bkU+/PBDnTx50q3vFRfCOTVuEB8fr169eunRRx9VUVGRbrzxRi1btkyff/653n33XXl4eLit9qpVq3TixAnrm9UPP/ygDz/8UJLUp08fm8tJq+rVV1/Vv//9b91+++2644477JYb3fFD/cgjj6hevXrq2LGjAgMDVVBQoA8++ECpqal6+umnrZdOVicfHx9169bNrn3RokXy8PBw+Fh1GDx4sPUwm7+/v/bs2aNXX31Vf/75pxYtWuSWmnFxcerbt6+mTJmisrIyRUVFafv27Zo8ebLuvPNOt745/u///q8OHTrk9lUaSUpISFC/fv3Uq1cvPfXUU/L399fWrVs1bdo0hYeHWw+3Vaddu3ZpxYoVioyMlLe3t7777jv95z//qfa7NVfmPWDy5Mnq0KGD7rzzTo0fP16nT5/Wv//9b/n7++tf//qXW2oePHjQelivfJVo1apVCggIUEBAgLp27VqtNS0Wi3r37q3MzEwlJyertLTU5j0qICDA5iTx6qh55swZ9erVS4MHD9ZNN92kWrVq6eeff9asWbNUXFzs0h9+F6sZGhqq0NBQh/s2adLE5feni9U9ePCgBg8erIEDB+rGG2+UxWLRhg0blJycrFatWl2S/8cOXc6b5JjZsWPHjCeeeMIICgoyvLy8jFtvvdVYtmyZ2+uGhIQYkhxurt7oqiJdu3atsJa7frTefvttIzY21vD39zc8PT2N6667zujatavTN9KqDu6+8dS0adOMdu3aGX5+foaHh4cREBBg3H333ca2bdvcVtMwDOPkyZPGs88+awQHBxuenp5Gs2bNjMTEROP06dNurdurVy/D19fXKCoqcmudcl9++aURFxdnBAUFGbVq1TJuvvlm41//+pfDG7ZVh59++sno0qWL0aBBA8PLy8u48cYbjeeff944fvx4tdap7HvA9u3bjR49ehi1a9c26tWrZ/Tr18/uZoTVWbP8ZpKOtq5du1Z7zX379l3w/Wno0KHVXvP06dPGiBEjjJYtWxp16tQxPD09jaZNmxoPPvig8f333ztdrzI1K6Iq3HyvMnUPHTpk3H333UZoaKhRq1Ytw8vLy7jpppuMZ555xjhy5IjLdavKYhhuuvc5AADAJcQ5NQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBQINQAAwBT+f8TxZySU2st5AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X))\n",
    "x2 = X\n",
    "x3 = list(np.arange(X+1,n+1))\n",
    "plt.bar(x1, nbinom.pmf(x1, p=p, n=r), color ='gray')\n",
    "plt.bar(x2, nbinom.pmf(x2, p=p, n=r), color ='#DFFF00')\n",
    "plt.bar(x3, nbinom.pmf(x3, p=p, n=r), color ='gray')\n",
    "plt.xlim(-1,n+1)\n",
    "plt.xticks(np.arange(0,n+1), fontsize=12, ha='center')\n",
    "plt.title(f'NB({r}, {p})')\n",
    "prob = np.sum([nbinom.pmf(x2, p=p, n=r)])\n",
    "plt.text(8, 0.02, f'$P({np.round(X, 3)}) = $ {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XMMnBa5iJUpD"
   },
   "source": [
    "<a name='Geometric_Distribution'></a>\n",
    "\n",
    "## **2.4. Geometric Distribution:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7v4WrQTfYtww"
   },
   "source": [
    "The geometric distribution is a special case of the negative binomial distribution.\n",
    "\n",
    "Suppose now that $n$ independent trials, each of which results in a “success” with probability $p$ and in a “failure” with probability $1 − p$, are to be performed. If $X$ represents the number of experiemnts to the occurrence of the fisrt success, then $X$ is said to be a geometric random variable with parameter $(p)$.\n",
    "\n",
    "$P(X=i) = (1-p)^{i-1}\\ p \\quad \\quad i = 1,2,...,\\infty$\n",
    "\n",
    "$\\\\ $\n",
    "\n",
    "$E(X) = \\frac{1}{p}$\n",
    "\n",
    "$Var(X) = \\frac{1-p}{p^2} = \\frac{q}{P^2}$\n",
    "\n",
    "$Median(X) = \\lceil \\frac{-1}{log_2 (1-p)} \\rceil$\n",
    "\n",
    "$Skewness(X) = \\frac{2\\ -\\ p}{\\sqrt{1\\ -\\ p}}$\n",
    "\n",
    "$Kurtosis(X) = 6+ \\frac{p^2}{1\\ -\\ p}$\n",
    "\n",
    "$\\\\ $\n",
    "\n",
    "Moment-generating function:\n",
    "\n",
    "$M_{x}(t) = \\frac{p\\ e^t}{1\\ -\\ q\\ e^t}$\n",
    "\n",
    "$\\\\ $\n",
    "\n",
    "$CDF = F(X=x) = 1-q^x$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "-zniiZHOJaki",
    "outputId": "1ddba456-6ff0-49d8-dd52-3e822f762440"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "N = 1000000\n",
    "p = 0.6\n",
    "\n",
    "geo_data = np.random.geometric(p = p, size = N)\n",
    "\n",
    "sns.histplot(geo_data, color='orange', stat='density', bins=50)\n",
    "\n",
    "plt.xlim(1,15)\n",
    "plt.xticks(list(range(1,15)), fontsize=12, ha='center')\n",
    "plt.title('Geometric Distribution');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "7n0s2hHUilT8",
    "outputId": "ece50203-effb-4cad-d962-01c9b7c10feb"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the G(0.6) Distribution is:  1.6667\n",
      "The median of the G(0.6) Distribution is:  1.0\n",
      "The variance of the G(0.6) Distribution is:  1.1111\n",
      "The standard deviation of the G(0.6) Distribution is:  1.0541\n",
      "The skewness of the G(0.6) Distribution is:  2.2136\n",
      "The kurtosis of the G(0.6) Distribution is:  6.9\n"
     ]
    }
   ],
   "source": [
    "p = 0.6\n",
    "print(f'The mean of the G({p}) Distribution is: ', np.round(geom.mean(p = p), 4))\n",
    "print(f'The median of the G({p}) Distribution is: ', np.round(geom.median(p = p), 4))\n",
    "print(f'The variance of the G({p}) Distribution is: ', np.round(geom.var(p = p), 4))\n",
    "print(f'The standard deviation of the G({p}) Distribution is: ', np.round(geom.std(p = p), 4))\n",
    "print(f'The skewness of the G({p}) Distribution is: ', np.round(geom.stats(p = p, moments='mvsk')[2], 4))\n",
    "print(f'The kurtosis of the G({p}) Distribution is: ', np.round(geom.stats(p = p, moments='mvsk')[3], 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ktPXTBJfItDJ"
   },
   "source": [
    "Integrating the PDF, gives us the cumulative distribution function (CDF) which is a function that maps values to their percentile rank in a distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "id": "0HIc4gGnMmcY",
    "outputId": "f7328e7f-52a0-498b-8ecf-484afbf3aa37"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 6\n",
    "x = np.arange(0, n, 0.001)\n",
    "x1 = np.arange(0, n)\n",
    "x2 = np.arange(0, n-1) + 0.999\n",
    "\n",
    "plt.scatter(x, geom.cdf(x, p=p), color = 'r')\n",
    "plt.scatter(x2, geom.cdf(x2, p=p), color = 'white', edgecolor='black', s=100)\n",
    "plt.scatter(x1, geom.cdf(x1, p=p), color = 'black', edgecolor='black', s=100)\n",
    "plt.xlim(-0.1,n);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QX0gpNAcjkxZ"
   },
   "source": [
    "To find the left probability of a point use the code below:\n",
    "\n",
    "''\n",
    "geom.cdf($X,P$)\n",
    "''\n",
    "\n",
    "To find the right probability of a point use the code below:\n",
    "\n",
    "''\n",
    "geom.sf($X,P$)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "TDv634j5jkxb",
    "outputId": "4294f0ad-6d1a-4ad1-a8fc-d197da3da4e8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The left probability of *3* in the G(0.6) Distribution is:  0.9359999999999999\n",
      "The Right probability of *3* in the G(0.6) Distribution is:  0.06400000000000002\n"
     ]
    }
   ],
   "source": [
    "X = 3\n",
    "p = 0.6\n",
    "print(f'The left probability of *{X}* in the G({p}) Distribution is: ', geom.cdf(X, p=p))\n",
    "print(f'The Right probability of *{X}* in the G({p}) Distribution is: ', geom.sf(X, p=p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Fyxvnvnokj0G"
   },
   "source": [
    "To find the probability between two points $[X,Y]$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "DOoHBL7-kj0G",
    "outputId": "ee0d22b9-8b10-429a-e2dd-aec7a009169a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *[2, 4]* in the G(0.6) Distribution is:  0.3744\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "Y = 4\n",
    "p = 0.6\n",
    "xs = np.arange(X, Y+1)\n",
    "print(f'The probability between *[{X}, {Y}]* in the G({p}) Distribution is: ', np.sum([geom.pmf(xs, p=p) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "LByIeWG_kj0I",
    "outputId": "eea9a2f3-8fce-4cb7-b214-4c132c0e1a7c"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(1,X))\n",
    "x2 = list(np.arange(X,Y+1))\n",
    "x3 = list(np.arange(Y+1,Y+10))\n",
    "plt.bar(x1, geom.pmf(x1, p=p), color ='gray')\n",
    "plt.bar(x2, geom.pmf(x2, p=p), color ='#DFFF00')\n",
    "plt.bar(x3, geom.pmf(x3, p=p), color ='gray')\n",
    "plt.xlim(0,10)\n",
    "plt.xticks(np.arange(0,Y+10), fontsize=12, ha='center')\n",
    "plt.title(f'G({p})')\n",
    "xs = np.arange(X, Y+1)\n",
    "prob = np.sum([geom.pmf(xs, p=p) for xs in xs])\n",
    "plt.text(8.5, 0.02, f'$P({np.round(X, 3)} \\leq X \\leq {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "u1GuWGA-mJrf"
   },
   "source": [
    "To find the probability between two points $(X,Y)$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "1efpZjPNmJrg",
    "outputId": "8c4351e2-ad4a-4c0d-d886-3017bd024401"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *(2, 4)* in the Normal Standard Distribution is:  0.09600000000000002\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "Y = 4\n",
    "p = 0.6\n",
    "xs = np.arange(X+1, Y)\n",
    "print(f'The probability between *({X}, {Y})* in the Normal Standard Distribution is: ', np.sum([geom.pmf(xs, p=p) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "6n-Cnw9HmJrh",
    "outputId": "202bb04a-ea53-4a10-a92d-a4ec6f5a0d76"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(1,X+1))\n",
    "x2 = list(np.arange(X+1,Y))\n",
    "x3 = list(np.arange(Y,Y+10))\n",
    "plt.bar(x1, geom.pmf(x1, p=p), color ='gray')\n",
    "plt.bar(x2, geom.pmf(x2, p=p), color ='#DFFF00')\n",
    "plt.bar(x3, geom.pmf(x3, p=p), color ='gray')\n",
    "plt.xlim(0,10)\n",
    "plt.xticks(np.arange(0,Y+10), fontsize=12, ha='center')\n",
    "plt.title(f'G({p})')\n",
    "xs = np.arange(X+1, Y)\n",
    "prob = np.sum([geom.pmf(xs, p=p) for xs in xs])\n",
    "plt.text(8.5, 0.02, f'$P({np.round(X, 3)} < X < {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dY81LwTLnLIO"
   },
   "source": [
    "To find the probability between two points $[X,Y)$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "wADy_TTTnLIP",
    "outputId": "a82d6b30-8091-48be-870f-3fbc351906cb"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *[2, 4)* in the G(0.6) Distribution is:  0.336\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "Y = 4\n",
    "p = 0.6\n",
    "xs = np.arange(X, Y)\n",
    "print(f'The probability between *[{X}, {Y})* in the G({p}) Distribution is: ', np.sum([geom.pmf(xs, p=p) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "WhrahEjanLIQ",
    "outputId": "90d6ec58-b34c-4b33-e040-a8e850580e40"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lOjpaderUkYeHh0JCQrR3795irbd//365uLioRYsWJdktAAC4x9kdXNavX6+JEydqxowZiouLU8eOHRUWFqb4+Pgi10tNTdWQIUPUrVu3EhcLAADubXYHl/nz52vEiBEaOXKkgoODtWDBAgUGBmrhwoVFrjdq1CgNHDhQ7dq1K3GxAADg3mZXcMnKytLhw4cVGhpq0x4aGqoDBw4Uut7777+vkydPKjIyslj7yczMVFpams0CAABgV3BJTk5WTk6OAgICbNoDAgKUlJRU4Do//fSTpk+frjVr1sjFxaVY+5kzZ458fHysS2BgoD1lAgCAu1SJLs61WCw2rw3DyNcmSTk5ORo4cKCioqLUoEGDYm8/IiJCqamp1uXMmTMlKRMAANxlijcE8v/z8/OTs7NzvtGV8+fP5xuFkaTLly/r0KFDiouL0/jx4yVJubm5MgxDLi4u2r59ux566KF867m7u8vd3d2e0gAAwD3ArhEXNzc3hYSEKDY21qY9NjZW7du3z9ff29tb3377rY4cOWJdRo8erYYNG+rIkSNq06bNrVUPAADuKXaNuEjSpEmTNHjwYLVu3Vrt2rXTkiVLFB8fr9GjR0u6cZonISFBK1eulJOTk5o2bWqzfpUqVeTh4ZGvHQAA4GbsDi79+/dXSkqKZs+ercTERDVt2lQxMTEKCgqSJCUmJt50ThcAAICSsBiGYTi6iJtJS0uTj4+PUlNT5e3tXerbj4qKKvVtFkdxbw8HAMCMbsfnN88qAgAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAApkFwAQAAplGi4BIdHa06derIw8NDISEh2rt3b6F99+3bpw4dOsjX11eenp5q1KiR3nzzzRIXDAAA7l0u9q6wfv16TZw4UdHR0erQoYMWL16ssLAwHT9+XLVq1crX38vLS+PHj1fz5s3l5eWlffv2adSoUfLy8tLTTz9dKgcBAADuDRbDMAx7VmjTpo1atWqlhQsXWtuCg4PVp08fzZkzp1jb6Nu3r7y8vLRq1api9U9LS5OPj49SU1Pl7e1tT7nFEhUVVerbLI7IyEiH7BcAgDvhdnx+23WqKCsrS4cPH1ZoaKhNe2hoqA4cOFCsbcTFxenAgQPq3LlzoX0yMzOVlpZmswAAANgVXJKTk5WTk6OAgACb9oCAACUlJRW5bs2aNeXu7q7WrVtr3LhxGjlyZKF958yZIx8fH+sSGBhoT5kAAOAuVaKLcy0Wi81rwzDytf3Z3r17dejQIS1atEgLFizQunXrCu0bERGh1NRU63LmzJmSlAkAAO4ydl2c6+fnJ2dn53yjK+fPn883CvNnderUkSQ1a9ZMv/32m2bNmqUnnniiwL7u7u5yd3e3pzQAAHAPsGvExc3NTSEhIYqNjbVpj42NVfv27Yu9HcMwlJmZac+uAQAA7L8detKkSRo8eLBat26tdu3aacmSJYqPj9fo0aMl3TjNk5CQoJUrV0qS3n33XdWqVUuNGjWSdGNelzfeeEMTJkwoxcMAAAD3AruDS//+/ZWSkqLZs2crMTFRTZs2VUxMjIKCgiRJiYmJio+Pt/bPzc1VRESETp06JRcXF9WtW1dz587VqFGjSu8oAADAPcHueVwcgXlcAAAwH4fP4wIAAOBIBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaBBcAAGAaLo4uAIU7LYtD9ltbhkP2CwDAzTDiAgAATIPgAgAATIPgAgAATIPgAgAATIPgAgAATIPgAgAATIPgAgAATIPgAgAATIPgAgAATIPgAgAATIPgAgAATIPgAgAATIPgAgAATIPgAgAATIPgAgAATIPgAgAATIPgAgAATIPgAgAATIPgAgAATKNEwSU6Olp16tSRh4eHQkJCtHfv3kL7fvTRR+rRo4f8/f3l7e2tdu3aadu2bSUuGAAA3LvsDi7r16/XxIkTNWPGDMXFxaljx44KCwtTfHx8gf337NmjHj16KCYmRocPH1bXrl3Vu3dvxcXF3XLxAADg3mIxDMOwZ4U2bdqoVatWWrhwobUtODhYffr00Zw5c4q1jSZNmqh///568cUXi9U/LS1NPj4+Sk1Nlbe3tz3lFktUVFSpb7M4IiMji3z/tCx3qBJbtWXXjwQAAAW6HZ/fdo24ZGVl6fDhwwoNDbVpDw0N1YEDB4q1jdzcXF2+fFmVK1cutE9mZqbS0tJsFgAAALuCS3JysnJychQQEGDTHhAQoKSkpGJtY968ebpy5Yoef/zxQvvMmTNHPj4+1iUwMNCeMgEAwF2qRBfnWiy2pzAMw8jXVpB169Zp1qxZWr9+vapUqVJov4iICKWmplqXM2fOlKRMAABwl3Gxp7Ofn5+cnZ3zja6cP38+3yjMn61fv14jRozQhg0b1L179yL7uru7y93d3Z7SAADAPcCuERc3NzeFhIQoNjbWpj02Nlbt27cvdL1169bpr3/9q9auXatevXqVrFIAAHDPs2vERZImTZqkwYMHq3Xr1mrXrp2WLFmi+Ph4jR49WtKN0zwJCQlauXKlpBuhZciQIXrrrbfUtm1b62iNp6enfHx8SvFQAADA3c7u4NK/f3+lpKRo9uzZSkxMVNOmTRUTE6OgoCBJUmJios2cLosXL1Z2drbGjRuncePGWduHDh2qFStW3PoRAACAe4bdwUWSxo4dq7Fjxxb43p/DyO7du0uyCwAAgHx4VhEAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADANggsAADCNEgWX6Oho1alTRx4eHgoJCdHevXsL7ZuYmKiBAweqYcOGcnJy0sSJE0taKwAAuMfZHVzWr1+viRMnasaMGYqLi1PHjh0VFham+Pj4AvtnZmbK399fM2bM0P3333/LBQMAgHuX3cFl/vz5GjFihEaOHKng4GAtWLBAgYGBWrhwYYH9a9eurbfeektDhgyRj4/PLRcMAADuXXYFl6ysLB0+fFihoaE27aGhoTpw4ECpFZWZmam0tDSbBQAAwK7gkpycrJycHAUEBNi0BwQEKCkpqdSKmjNnjnx8fKxLYGBgqW0bAJDfzJkzZbFY9Nprrzm6FJSShx9+WBaLRTt37nR0KaWqRBfnWiwWm9eGYeRruxURERFKTU21LmfOnCm1bQPA3ahWrVqyWCz5lnLlyqlx48Z67rnn9Pvvvxe47tmzZzV//nz5+/tr3LhxNu+lpKTo/fff15NPPqnGjRvLy8tL7u7uqlmzpvr06aPNmzfficMrsU2bNsliscjJyUnfffddof2ys7MVFhYmi8WiChUq6MiRI3euSDvNnTvX5ntcmFmzZkmSJk+erNzc3DtU3e3nYk9nPz8/OTs75xtdOX/+fL5RmFvh7u4ud3f3UtseStdplV5ItVdtGQ7bN1BWpaSkWP/Aq1Spktzc3CTd+DBOSUnRiRMndOLECa1fv14HDx7MN4o9Y8YMZWRkaPbs2fLy8rJ5r2rVqsrOzra+9vDwkKurqxISEpSQkKB//etfCgsL08aNG1WuXLnbfKT269u3rxo3bqzjx49rzpw5Wr16dYH9xo0bp61bt8rFxUUbNmxQixYt7myhxfTDDz8oKiqqWH3btm2rnj17atu2bVq9erWGDBlym6u7M+wacXFzc1NISIhiY2Nt2mNjY9W+fftSLQwAUDyHDx+2fr1r1y4lJSUpKSlJycnJunDhgkaPHi1JSkhI0IwZM2zWTUhI0Jo1a+Tm5qbhw4fn23Z2drYefPBBRUdH6+TJk8rIyFB6erpOnTqlESNGSJK2bNmiUaNG3cYjLDmLxaLnn39ekvThhx/q5MmT+frMmTNHS5YskXRjuo+HH374jtZYXLm5uRoxYoSuXbumdu3aFWudvO/93XQK0O5TRZMmTdJ7772n5cuX68SJE3r22WcVHx9v/ceJiIjIl+qOHDmiI0eOKD09Xb///ruOHDmi48ePl84RAMA9Li+4uLq6Kjg42Oa9SpUq6d1331WTJk0kSTExMTbvL126VDk5OQoPD1flypXzbXvnzp36+uuvNWbMGN13333W9tq1a+u9996zBpbVq1ff9tP6aWlp+uijj/Tzzz/btd6AAQNUt25d5eTk6NVXX7V5b926ddYw9/zzz+upp54qtXr/LDc3V7t27dKvv/5aovXfeecd7d+/X4MGDcp3k0xh8r6v3333nfbv31+i/ZY1dgeX/v37a8GCBZo9e7ZatGihPXv2KCYmRkFBQZJuTDj35zldWrZsqZYtW+rw4cNau3atWrZsqfDw8NI5AgC4x33zzTeSpMaNG1tPE/2Rk5OTHnjgAUk3Tivl5ORIunF94rJlyyRJAwcOLHDbXbt2LXLfeaMuknTo0CH7i7+Jo0eP6tVXX1WXLl3k6+urfv362R1cnJ2dNX36dEnSBx98oLNnz0qS9u7dq2HDhskwDA0cOFAvvfRSqdcvScePH1dERIRq166thx56SKdOnbJ7G6dOndKMGTPk6+urN998s9jrubm5qV+/fpJkHVUyO7uucckzduxYjR07tsD3VqxYka/NMLguAQBul7wRl6Im+czKypIklS9fXs7OzpKkY8eOWT/EO3bsWKJ9e3h4WL/OC0S3Ii0tTV988YViYmK0detWJSQk2LzfrFkz1ahRw+7tDh06VLNnz9aZM2f0xhtvaMyYMerTp48yMzPVuXNnvf/++6V6k8n58+e1bt06rVq1yuZUXqVKlQoc2bqZp556SleuXFF0dLT8/f3tWrdTp05aunSptm7davd+y6ISBRcAQNlw8eJF61/whQUXwzB08OBBSVKrVq2s7Xv27JEkBQYGqmrVqiXa/+7du61fN2vWrETbOHr0qLZs2aItW7Zo//79NhcDly9fXg899JB69eql8PBw1axZs0T7cHV11dSpUzVhwgQtXbpUn3zyiS5cuKDg4GBt3ry5wJEqe2VkZOhf//qXVq1ape3bt1uPw8PDQ4888ogGDRqk8PBwu/e1dOlS7dixQ927dy/RBbZt2rSRdCNMff/992rUqJHd2yhLCC4AYGJ5p4kkFXonzOLFi63hZujQodb2r7/+WlLRIzVFuXTpkubMmSPpxohNw4YNi7Veenq6tm3bZg0r586ds3m/QYMGCg8PV3h4uDp37lwqoUKSRo4cqZdffllJSUk6deqUAgICFBMTo0qVKpV4m4Zh6Msvv9SqVau0ceNG64SpTk5OeuihhzRo0CD9v//3/+Tt7V2i7SckJGjKlCny9PTU4sWLS7SN+vXrq3z58kpPT9fBgwcJLgAAx/ljcPljAMnKytJPP/2k5cuXa8GCBZKkhx56yCa45AUGe089SDcuNB08eLASExPl7u6ud955p9jrbty4UcOGDbO+9vDwUJcuXRQeHq5evXrZXARcmlxdXVWvXj3rlB6rVq1S7dq1S7StEydOaNWqVVqzZo3NdZ0tWrTQk08+qSeeeELVq1e/5ZpHjRql1NRUvfrqq7f07+Lr66v09PR8IdGMCC4AYGJ/vH7Cz8+v0H4DBw7U4sWLrde3SLJOSFeSay6eeeYZffbZZ5Ju3EJ8Kw/RzcnJ0bVr13Tt2jVdvXq1xNu5mfHjx2vfvn3W13v37lWPHj3s3s769es1YMAA6+vatWtr4MCBGjRokBo3blwqtUo37tT6/PPP1aJFC02aNOmWtlW5cmX9+uuvhU5CaCYlmjkXAFA25I24lCtXTgEBAQoICFDVqlVVr149dezYUZMnT1ZcXJzWrFmj8uXL26x77do1SbJ7ws/JkyfrH//4hyTpzTffLHD+l6IMGjRIO3fu1JQpU9SkSRNdv35du3fv1tSpU9WsWTMFBgbq6aef1ubNm0vtWXVz5szRokWLJMk6B8o777xTou1nZGRYv/b09NTjjz+uAQMGlGpoOX/+vCZOnChnZ2ctXbpULi63Ns7g6ekp6f++52ZGcAEAk0pLS7PeGjxr1izrxHOJiYn66aeftGfPHr3++uuFXvvi6+sr6cYFvsU1depUzZs3T5L0+uuva+LEiXbX7erqqq5du+q1117TsWPHFB8fr0WLFul//ud/VL58eZ09e1ZLly5V37595efnZ+377bff2r0vSVqzZo11rpYXX3xRn376qcqXL69Lly4pOjra7u2FhYUpKipK9evXV0ZGhl577TU1b95czZo109y5c0s8T8sfTZs2TSkpKXr66afVqFEjpaen2yx5d4lJKrDtzy5cuCDp/77nZkZwAQCTiouLs0430bp1a7vXz7u2Je9D7WamTJmi119/XdKNmVgnT55s9z4LEhgYqFGjRulf//qXUlJSFBsbq0mTJqlRo0bW0Zhp06apefPmqlmzps3psZvZuXOnhg8fLsMwNHToUEVFRcnX19c6aeqbb75pM4JSHAEBAXrxxRf1448/6uDBgxo7dqx8fX117NgxRUREqE6dOurYsaMWLVqklJQUu7adJ+9i6oULF6pChQr5lryLoiVZ26ZOnVro9vK+xyW5nqmsIbgAgEnlnSayWCw2tzkXV96pjV9++eWmfSdPnqw33nhD0o3QMmXKFLv3Vxxubm7q3r275s2bpxMnTujUqVN699131atXL5UrV04JCQnFvk7j2LFj6tu3r7KystSjRw8tXbrU5ng8PDx0/vx5m3Z7tW3bVu+++64SExO1efNm9e3bV25ubtq3b5/GjBmjatWqqXfv3vrwww9v6/U7Rbl8+bKSk5MlKd/MymZEcAEAk8obeahbt658fHzsXr9Tp06SpP/+97/KzMwstN/kyZOtp4feeOON2xZaClK7dm2NHTtWn332mS5cuKCtW7cW67brhIQEhYWFKTU1Vffff782btwoV1dX6/sBAQEaOXKkpBunvIo6zVIcrq6u6tOnjzZt2qTExEQtWrRIHTp00PXr1/XZZ5/piSeeUEBAgAYPHlysO3t2794twzAKXSIjI61989ry7h77s0OHDik3N1cuLi7q0KHDLR1nWUBwAQCTyhtxKclpIknq0KGDXFxclJWVpSNHjhTYZ9q0adbQMn/+fD333HMl2tcfZWZmKjk52e7l8uXLCgkJuekkdGlpaQoPD9fZs2cVGBiozz//vMB5VKZNmyY3NzedPXtWK1euvOXjylOpUiWNGjVK+/bt08mTJzVr1izVq1dP6enpWr16tX788cdS21dx5M3X06pVq3wXaJsRwQUATOjKlSv64YcfJEkhISEl2oa3t7d69eolSfrkk0/yvR8fH299qrCTk5NeffVVVa1atdAl71TSzaxbt07+/v4lXnbs2FHotq9fv66+ffvq6NGj8vHxUUxMTKGPCKhZs6Z1Jtq5c+eWyiML/uy+++5TZGSkfvrpJx04cEBjxoy54+Eh73tb2POozIbgAgAmdOTIEeXm5koqeXCRZH2689q1a/M9Vy5v+3lf//bbb0Uu6enpJa6jtIwYMUI7duyQq6urPvroIzVt2rTI/hEREXJxcdHJkye1fv3621pbu3btFB0dXeIRspI4deqUDh48KE9PzxI9LqAsshgmeAJiWlqafHx8lJqaWuJpk4sSFRVV6tssjj+eoyzIaZXeA7/sUVtF/0g4qi7p5rUBsE9ubq4aNGigkydP6ssvv7Re94K7w+zZsxUZGalhw4Zp+fLld3z/t+PzmxEXALiHOTk56e9//7ukG6dLcPe4cuWK3nnnHbm7u9/0D2UzIbgAwD1uwIABevDBB7VlyxbrhZwwv3/84x9KTk7W3/72NwUFBTm6nFLDs4oA4B5nsVi0ePFiffzxx9b5PmB+Xl5emjVrVolmNy7LCC4AALVo0aLQRwPAnMaPH+/oEm4LThUBAADTILgAAADTILgAAADTILgAAADTILgAAADTILgAwF3u8uXLmjVrlpo1a6by5cvLx8dHDzzwgObNm3dLT0X+8ssvNWPGDPXs2VP169dXpUqV5OrqqipVqqhr1656++23lZGRYfd2w8LCZLFYZLFY1KVLlxLXh7sTt0MDwF3s119/VZcuXXT69GlJUrly5ZSZmalDhw7p0KFDWrNmjXbs2KFKlSrZve3XX39dn3/+ufW1l5eX3N3d9fvvv2v37t3avXu3FixYoK1bt6pBgwbF2uaKFSu0detWu2vBvYMRFwC4S+Xk5Kh37946ffq0qlWrptjYWF25ckVXr17Vhx9+qAoVKiguLk6DBg0q0fa7d++ut99+W998843S0tKUnp6u9PR0JScn6+2335anp6dOnTqlRx991OaBjYVJSkrSpEmTVLFiRQUHB5eoJtz9CC4AcJdasWKFvv32W0nSpk2b1L17d0k3nk/Uv39/LV68WJK0ZcsW7dixw+7tT5w4URMmTFDLli1VoUIFa7uvr68mTJigBQsWSJKOHz+ugwcP3nR7Y8eO1cWLF/X666+rSpUqdteDewPBBQDuUh988IEkqWvXrmrXrl2+9wcMGKA6depIklauXFnq+2/btq3167NnzxbZ95///Kc2b96szp07a8SIEaVeC+4eBBcAuAtdvXpV+/fvl3TjYteCWCwWPfzww5Kk7du3l3oNe/futX5dt27dQvulpKRowoQJcnd315IlS2SxWEq9Ftw9uDgXAO5CJ06csF5X0rRp00L75b2XlJSkCxcuqHLlyre034yMDJ09e1YbNmzQ7NmzJUmdOnVS69atC13nb3/7m86fP6+XXnqp2Bfx4t5FcMFdIyoqymH7joyMdNi+gYKcO3fO+nWNGjUK7ffH986dO1ei4JKUlKRq1aoV+F7v3r21YsWKQtf99NNPtXbtWjVt2lRTp061e9+493CqCADuQpcvX7Z+Xa5cuUL7/fG9P65jD2dnZwUEBCggIEAeHh7W9scee0yvvfZaoWEoNTVVY8aMkZOTk5YuXSpXV9cS7R/3FoILAOCW+Pv7KykpSUlJSbp69arOnDmjGTNm6NNPP1Xz5s21ZMmSAtd77rnnlJCQoLFjx9pcyAsUheACAHehP96efPXq1UL7/fG9P65TUhaLRTVr1tRLL72kNWvW6Pr16xozZoz++9//2vT74osvtGzZMtWsWVOvvPLKLe8X9w6CCwDchapXr279OiEhodB+f3zvj+uUhr59+yooKEi5ublatmyZzXtPPfWUJOm1116TxWKxTl6Xt+Tk5Ei6MYnen9twbyO4AMBdKDg4WE5ON37FHzt2rNB+ee9VrVr1lu8oKkheGPr5559t2vMeQTBw4EBVqFAh37Jv3z5J0r59+6xtn376aanXB/MhuADAXahcuXLq0KGDJBX67B/DMLRt2zZJUmhoaKnXYBiGTp06Jal0TkMBEsEFAO5aQ4cOlSTt2rVLX3/9db73N2zYoF9++UWSNGTIELu2nZ2dfdM+77//vpKSkiQp31OeDcMocuncubMkqXPnzta2Pn362FUj7k4EFwC4Sw0dOlTNmjWTYRjq16+f9XlEubm52rBhg/U6k7CwMHXr1i3f+rNmzZLFYpHFYrGe2smzb98+derUSatWrco3nf9PP/2k6dOna9SoUZJuzJr717/+tfQPEPckJqADgLuUi4uLPvnkE3Xt2lWnT59W9+7dVa5cOeXm5uratWuSpJYtW2rNmjUl2v7evXut0/p7eHiofPnyunLlijIyMqx97r//fn388cfy9PS89QMCxIgLANzVateuraNHj+rFF19U06ZNZbFY5OrqqpCQEL3xxhv66quvVKlSJbu3GxISopUrV2r48OG6//775ePjo0uXLsnJyUl169bVY489pg8//FCHDx9W7dq1S//AcM+yGIZhOLqIm0lLS5OPj49SU1Pl7e1d6tt31FTxN5sm/rQc86Cx2ir6R8JRdUlF18aU/wBQttyOz29GXAAAgGlwjQtwmzESBAClhxEXAABgGgQXAABgGgQXAABgGgQXAABgGiUKLtHR0apTp448PDwUEhJinYCoMF9++aVCQkLk4eGh++67T4sWLSpRsQAA4N5m911F69ev18SJExUdHa0OHTpo8eLFCgsL0/Hjx1WrVq18/U+dOqXw8HA99dRTWr16tfbv36+xY8fK399f/fr1K5WDAFAyZXUOIwAojN0jLvPnz9eIESM0cuRIBQcHa8GCBQoMDNTChQsL7L9o0SLVqlVLCxYsUHBwsEaOHKnhw4frjTfeuOXiAQDAvcWuEZesrCwdPnxY06dPt2kPDQ3VgQMHClzn4MGD+R6X3rNnTy1btkzXr1+Xq6trvnUyMzOVmZlpfZ2amirpxgx8t0PeMzvutJsdz+U7VMefpals1iUVXZujvo9S0d/LslqXVHZ/9gHcHfL+r5fqJP2GHRISEgxJxv79+23aX375ZaNBgwYFrlO/fn3j5Zdftmnbv3+/Ick4d+5cgetERkYaklhYWFhYWFjuguXkyZP2xI0ilWjmXIvF9lk1hmHka7tZ/4La80RERGjSpEnW15cuXVJQUJDi4+Pl4+NTkpJvi7S0NAUGBurMmTO35RlKJUVd9imrdUlltzbqsg912aes1iWV3drKal2pqamqVauWKleuXGrbtCu4+Pn5ydnZWUlJSTbt58+fV0BAQIHrVK1atcD+Li4u8vX1LXAdd3d3ubu752v38fEpU9+QPN7e3tRlB+qyX1mtjbrsQ132Kat1SWW3trJal5NT6c2+YteW3NzcFBISotjYWJv22NhYtW/fvsB12rVrl6//9u3b1bp16wKvbwEAACiM3RFo0qRJeu+997R8+XKdOHFCzz77rOLj4zV69GhJN07zDBkyxNp/9OjR+vXXXzVp0iSdOHFCy5cv17JlyzR58uTSOwoAAHBPsPsal/79+yslJUWzZ89WYmKimjZtqpiYGAUFBUmSEhMTFR8fb+1fp04dxcTE6Nlnn9W7776r6tWr6+2337ZrDhd3d3dFRkYWePrIkajLPtRlv7JaG3XZh7rsU1brkspubfdSXRbDKM17lAAAAG4fnlUEAABMg+ACAABMg+ACAABMg+ACAABMo0wHl/T0dE2cOFHVq1eXh4eHWrRooQ8//NDRZeny5cuaOnWqQkND5e/vL4vFolmzZjm0pp07d2r48OFq1KiRvLy8VKNGDf3v//6vDh8+7NC6jhw5ol69eqlWrVry9PRU5cqV1a5dO61evdqhdRXkvffek8ViUfny5R1ax+7du2WxWApcvvrqK4fWJkn79u1TeHi4KlWqJE9PT9WvX19///vfHVbPX//610L/vRz9bxYXF6c+ffqoevXqKleunBo1aqTZs2fr6tWrDqtJkv7973+rZ8+eqlChgsqXL6+uXbtq//79d7QGe36PfvPNN+revbvKly+vihUrqm/fvvrll18cWte+ffs0cuRIhYSEyN3dXRaLRadPn74tNRW3rpycHM2fP18PP/ywatasqXLlyik4OFjTp0/XpUuXHFaXJL399ttq27at/Pz85O7urlq1amnAgAH67rvv7N5nmQ4uffv21QcffKDIyEht2bJFDzzwgJ544gmtXbvWoXWlpKRoyZIlyszMVJ8+fRxaS56FCxfq9OnTeuaZZxQTE6O33npL58+fV9u2bbVz506H1XXp0iUFBgbqlVdeUUxMjFauXKnatWtr8ODBeumllxxW158lJCRo8uTJql69uqNLsXrllVd08OBBm6Vp06YOrWnt2rXq3LmzfHx8tHLlSsXExGjatGml+wA1O73wwgv5/p0OHjwoPz8/1ahRQw888IBD6jp+/Ljat2+v06dPa8GCBfrss880YMAAzZ49W0888YRDapKk//znP+rUqZMyMjK0atUqrVq1SteuXVO3bt108ODBO1ZHcX+Pfv/99+rSpYuysrL0z3/+U8uXL9ePP/6ojh076vfff3dYXTt27NAXX3yhWrVqFToB652uKyMjQ7NmzVJQUJAWLFigmJgYPfXUU1qyZIk6dOigjIwMh9SV1y8sLEzvvfeetm/frqioKMXFxalNmzb64Ycf7NtpqT31qJR9/vnnhiRj7dq1Nu09evQwqlevbmRnZzuoMsPIzc01cnNzDcMwjN9//92QZERGRjqsHsMwjN9++y1f2+XLl42AgACjW7duDqioaG3atDECAwMdXYbVI488YvTu3dsYOnSo4eXl5dBadu3aZUgyNmzY4NA6/uzs2bOGl5eXMWbMGEeXclO7d+82JBkzZ850WA0zZswwJBk///yzTfvTTz9tSDIuXLjgkLp69uxpBAQEGFeuXLG2paWlGX5+fkb79u3vWB3F/T362GOPGX5+fkZqaqq17fTp04arq6sxdepUh9WVk5Nj/fr11183JBmnTp0q9XrsqSs7O9tITk7Ot+6GDRsMScaqVascUldhjh8/bkgyXnjhBbv2WWZHXDZv3qzy5cvrscces2kfNmyYzp07p6+//tpBlck6BF2WVKlSJV9b+fLl1bhxY505c8YBFRXNz89PLi4lesZnqVu9erW+/PJLRUdHO7qUMu29997TlStXNG3aNEeXclPLli2TxWLR8OHDHVZD3iNN/vxg2IoVK8rJyUlubm6OKEv79+9Xly5dVK5cOWtbhQoV1KlTJx04cECJiYl3pI7i/B7Nzs7WZ599pn79+tk8fycoKEhdu3bV5s2bHVKXVLrP3imO4tTl7Oxc4DMAH3zwQUm6LZ8Ft/J56O/vL0l2fxaU2eBy7NgxBQcH5zug5s2bW99H0VJTU/XNN9+oSZMmji5Fubm5ys7O1u+//67o6Ght27atTHwAnj9/XhMnTtTcuXNVs2ZNR5djY9y4cXJxcZG3t7d69uypffv2ObSePXv2qHLlyvr+++/VokULubi4qEqVKho9erTS0tIcWtsfpaamauPGjerWrZvq1KnjsDqGDh2qihUrasyYMfrll190+fJlffbZZ1q8eLHGjRsnLy8vh9SVlZVV4CymeW3ffvvtnS6pUCdPnlRGRob19/4fNW/eXD///LOuXbvmgMrMJe9ygbLwWZCTk6PMzEx9//33GjlypKpUqaJhw4bZtY0yG1xSUlIKfAx2XltKSsqdLsl0xo0bpytXrmjGjBmOLkVjx46Vq6urqlSpomeffVZvv/22Ro0a5eiyNHbsWDVs2FBjxoxxdClWPj4+euaZZ7R48WLt2rVLb731ls6cOaMuXbpo27ZtDqsrISFBV69e1WOPPab+/fvriy++0JQpU7Ry5UqFh4c79DqXP1q3bp0yMjI0YsQIh9ZRu3ZtHTx4UMeOHVPdunXl7e2t3r17a+jQoXrrrbccVlfjxo311VdfKTc319qWnZ1tHcUuS79b82op7LPAMAxdvHjxTpdlKgkJCZo+fbpat26tRx55xNHlyMvLSx4eHgoODtaJEye0e/duBQYG2rWNsjFWX4iihp/K2qmasuaFF17QmjVr9M477ygkJMTR5ej555/XyJEjdf78eX366acaP368rly54tCHbW7atEmffvqp4uLiytTPU8uWLdWyZUvr644dO+rRRx9Vs2bNNHXqVPXs2dMhdeXm5uratWuKjIzU9OnTJUldunSRm5ubJk6cqB07dqh79+4Oqe2Pli1bJl9fXz366KMOreP06dPq3bu3AgICtHHjRvn7++vrr7/WSy+9pPT0dC1btswhdU2YMEEjRozQ+PHjNWPGDOXm5ioqKkq//vqrpDt/CqQ4+CwomQsXLlj/qFi/fn2Z+N4eOHBAWVlZOnnypN5880117dpVO3bssGs0yPFHUQhfX98Ck/+FCxckFZzAcUNUVJReeuklvfzyyxo/fryjy5Ek1apVS61bt1Z4eLgWLlyop59+WhEREbflroDiSE9P17hx4zRhwgRVr15dly5d0qVLl5SVlSXpxt1QV65ccUhtBalYsaIeeeQRHT169LbcGVAceefO/xycwsLCJN24ZdXRjh49qkOHDunJJ590+MPmpk+frrS0NG3btk39+vVTp06dNGXKFC1YsEDLly/Xl19+6ZC6hg8frrlz52rVqlWqWbOmatWqpePHj1v/iKhRo4ZD6ipI3s9cYZ8FFotFFStWvMNVmcPFixfVo0cPJSQkKDY2Vvfdd5+jS5IktWrVSm3bttWgQYO0a9cuGYah559/3q5tlNng0qxZM504cULZ2dk27XnnXx19W2hZFRUVpVmzZmnWrFl2/zDcSQ8++KCys7Nv21wMN5OcnKzffvtN8+bNU6VKlazLunXrdOXKFVWqVEmDBg1ySG2FyTsV46i/MAu6zkD6v7rKwl9zeaMYI0eOdHAlN+Ywaty4cb5rWfJuz3bkdXrTpk1TcnKyvv32W50+fVoHDhzQxYsX5eXlVSZGaPPUrVtXnp6eBV538+2336pevXry8PBwQGVl28WLF9W9e3edOnVKsbGxhf7fdbQKFSqoUaNG+vHHH+1az/G/aQrx6KOPKj09XZs2bbJp/+CDD1S9enW1adPGQZWVXX//+981a9YszZw5U5GRkY4up0i7du2Sk5OTw/4KqFq1qnbt2pVv6dmzpzw8PLRr164yNc/MxYsX9dlnn6lFixYO+0Xdr18/SdKWLVts2mNiYiRJbdu2veM1/VFmZqZWr16tBx98sEz8YVO9enV99913Sk9Pt2nPmyvF0ReDu7u7q2nTpgoKClJ8fLzWr1+vp556Sp6eng6t649cXFzUu3dvffTRR7p8+bK1PT4+Xrt27VLfvn0dWF3ZlBdafvnlF23fvt3mtHNZkxee69WrZ9d6ZfYal7CwMPXo0UNjxoxRWlqa6tWrp3Xr1mnr1q1avXq1nJ2dHVrfli1bdOXKFet/puPHj2vjxo2SpPDwcJtbDe+EefPm6cUXX9TDDz+sXr165Zst1FEfKk8//bS8vb314IMPKiAgQMnJydqwYYPWr1+vKVOmWG+Hu9M8PDzUpUuXfO0rVqyQs7Nzge/dKQMHDrSeWvPz89NPP/2kefPm6bffftOKFSscVldoaKh69+6t2bNnKzc3V23bttWhQ4cUFRWlRx55RH/5y18cVpskffzxx7pw4UKZGG2RpIkTJ6pPnz7q0aOHnn32Wfn5+emrr77SnDlz1LhxY+sptjvt2LFj2rRpk1q3bi13d3f997//1dy5cx0yA3Jxfo9GRUXpgQce0COPPKLp06fr2rVrevHFF+Xn56fnnnvOYXX9/vvv1tN9eSNCW7Zskb+/v/z9/dW5c+c7XpfFYlHPnj0VFxenBQsWKDs72+azwN/fX3Xr1r3jdV2/fl09evTQwIEDVb9+fXl6eurHH3/UW2+9pczMTPv/0LZr1pc77PLly8bf/vY3o2rVqoabm5vRvHlzY926dY4uyzAMwwgKCjIkFbjczkmICtO5c+dC63Hkt3n58uVGx44dDT8/P8PFxcWoWLGi0blz59syEVJpKAsT0M2ZM8do0aKF4ePjYzg7Oxv+/v7Go48+avz73/92aF2GYRhXr141pk2bZgQGBhouLi5GrVq1jIiICOPatWuOLs3o0aOH4eXlZaSlpTm6FKudO3caoaGhRtWqVQ1PT0+jQYMGxnPPPVfgJGF3yg8//GB06tTJqFy5suHm5mbUq1fPmDlzppGenn7Haynu79FDhw4Z3bp1M8qVK2d4e3sbffr0yTex352uK2+iyIKWzp07O6SuU6dOFfk5MHToUIfUde3aNWPkyJFGcHCwUb58ecPFxcWoWbOm8eSTTxrfffed3fuzGEYZuYcRAADgJsrsNS4AAAB/RnABAACmQXABAACmQXABAACmQXABAACmQXABAACmQXABAACmQXABAACmQXABAACmQXABAACmQXABAACm8f8BZXejPr/yVboAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(1,X))\n",
    "x2 = list(np.arange(X,Y))\n",
    "x3 = list(np.arange(Y,n+1))\n",
    "plt.bar(x1, geom.pmf(x1, p=p), color ='gray')\n",
    "plt.bar(x2, geom.pmf(x2, p=p), color ='#DFFF00')\n",
    "plt.bar(x3, geom.pmf(x3, p=p), color ='gray')\n",
    "plt.xlim(0,10)\n",
    "plt.xticks(np.arange(0,Y+10), fontsize=12, ha='center')\n",
    "plt.title(f'G({p})')\n",
    "xs = np.arange(X, Y)\n",
    "prob = np.sum([geom.pmf(xs, p=p) for xs in xs])\n",
    "plt.text(8.5, 0.02, f'$P({np.round(X, 3)} \\leq X < {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qi58XxsXoJIS"
   },
   "source": [
    "To find the probability between two points $(X,Y]$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "dlEYv_COoJIT",
    "outputId": "f926f92a-47ed-4b3a-8d54-9f4b85c89066"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *(2, 4]* in the G(0.6) Distribution is:  0.13440000000000002\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "Y = 4\n",
    "p = 0.6\n",
    "xs = np.arange(X+1, Y+1)\n",
    "print(f'The probability between *({X}, {Y}]* in the G({p}) Distribution is: ', np.sum([geom.pmf(xs, p=p) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "O4Hm6-OVoJIU",
    "outputId": "b0185b1f-e393-40ec-cab7-8828ecefb138"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(1,X+1))\n",
    "x2 = list(np.arange(X+1,Y+1))\n",
    "x3 = list(np.arange(Y+1,Y+10))\n",
    "plt.bar(x1, geom.pmf(x1, p=p), color ='gray')\n",
    "plt.bar(x2, geom.pmf(x2, p=p), color ='#DFFF00')\n",
    "plt.bar(x3, geom.pmf(x3, p=p), color ='gray')\n",
    "plt.xlim(0,10)\n",
    "plt.xticks(np.arange(0,Y+10), fontsize=12, ha='center')\n",
    "plt.title(f'G({p})')\n",
    "xs = np.arange(X+1, Y+1)\n",
    "prob = np.sum([geom.pmf(xs, p=p) for xs in xs])\n",
    "plt.text(8., 0.02, f'$P({np.round(X, 3)} < X \\leq {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6DDYvsknpDYv"
   },
   "source": [
    "To find the probability of a point use the code below:\n",
    "\n",
    "''\n",
    "geom.pmf($X,P$)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "QZwbC5rJpDYw",
    "outputId": "7783f030-e27a-4ae6-cf02-4cc16dcc6dab"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of *X=2* in the G(0.6) Distribution is:  0.24\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "p = 0.6\n",
    "print(f'The probability of *X={X}* in the G({p}) Distribution is: ', geom.pmf(X, p=p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "qeG0Ppa5pDYy",
    "outputId": "1a4f3029-714b-4664-a4de-fe7c88fd0971"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Lk7e3tyIiIrRr165qrbd79255enqqZ8+eNdktAACo51wOLqmpqYqLi9P8+fOVkZGhAQMGKCYmRpmZmVWul5+fr/Hjx2vo0KE1LhYAANRvLgeXJUuWaNKkSZo8ebLCw8O1dOlSBQcHa/ny5VWuN2XKFI0dO1b9+vWrcbEAAKB+cym4FBUVaf/+/YqOjnZqj46O1p49eypd7/XXX9eRI0cUHx9frf0UFhaqoKDAaQEAAHApuOTm5qqkpERBQUFO7UFBQTp58mSF63z11VeaO3eu1q9fL09Pz2rtJykpSf7+/o4lODjYlTIBAMBNqkYX59psNqfvLcsq1yZJJSUlGjt2rBITE3XLLbdUe/vz5s1Tfn6+Yzl+/HhNygQAADeZ6g2B/P8CAgLk4eFRbnQlJyen3CiMJJ09e1b79u1TRkaGZs6cKUkqLS2VZVny9PTUtm3bdMcdd5Rbz263y263u1IaAACoB1wacfHy8lJERITS09Od2tPT09W/f/9y/f38/PTpp5/qwIEDjmXq1Knq3LmzDhw4oD59+lxb9QAAoF5xacRFkmbNmqVx48YpMjJS/fr104oVK5SZmampU6dKunyaJysrS2vWrFGDBg3UvXt3p/Vbtmwpb2/vcu0AAABX43JwiY2NVV5enhYuXKjs7Gx1795daWlpCg0NlSRlZ2dfdU4XAACAmrBZlmW5u4irKSgokL+/v/Lz8+Xn51fr209MTKz1bVZHdW8PBwDARNfj85tnFQEAAGMQXAAAgDEILgAAwBgEFwAAYAyCCwAAMAbBBQAAGIPgAgAAjEFwAQAAxiC4AAAAYxBcAACAMQguAADAGAQXAABgDIILAAAwBsEFAAAYg+ACAACMQXABAADGILgAAABjEFwAAIAxCC4AAMAYBBcAAGAMggsAADAGwQUAABiD4AIAAIxBcAEAAMYguAAAAGMQXAAAgDEILgAAwBgEFwAAYAyCCwAAMAbBBQAAGIPgAgAAjEFwAQAAxiC4AAAAYxBcAACAMQguAADAGAQXAABgDIILAAAwBsEFAAAYg+ACAACMQXABAADGILgAAABjEFwAAIAxCC4AAMAYBBcAAGAMggsAADAGwQUAABiD4AIAAIxRo+CSnJyssLAweXt7KyIiQrt27aq074cffqioqCi1aNFCPj4+6tKli1566aUaFwwAAOovT1dXSE1NVVxcnJKTkxUVFaWUlBTFxMTo0KFDCgkJKdff19dXM2fO1K233ipfX199+OGHmjJlinx9ffXYY4/VykEAAID6wWZZluXKCn369FGvXr20fPlyR1t4eLhGjx6tpKSkam3j3nvvla+vr9auXVut/gUFBfL391d+fr78/PxcKbdaEhMTa32b1REfH++W/QIAcCNcj89vl04VFRUVaf/+/YqOjnZqj46O1p49e6q1jYyMDO3Zs0eDBg2qtE9hYaEKCgqcFgAAAJeCS25urkpKShQUFOTUHhQUpJMnT1a5brt27WS32xUZGakZM2Zo8uTJlfZNSkqSv7+/YwkODnalTAAAcJOq0cW5NpvN6XvLssq1/dSuXbu0b98+vfrqq1q6dKk2btxYad958+YpPz/fsRw/frwmZQIAgJuMSxfnBgQEyMPDo9zoSk5OTrlRmJ8KCwuTJPXo0UOnTp1SQkKCHnzwwQr72u122e12V0oDAAD1gEsjLl5eXoqIiFB6erpTe3p6uvr371/t7ViWpcLCQld2DQAA4Prt0LNmzdK4ceMUGRmpfv36acWKFcrMzNTUqVMlXT7Nk5WVpTVr1kiSXnnlFYWEhKhLly6SLs/r8uKLL+rxxx+vxcMAAAD1gcvBJTY2Vnl5eVq4cKGys7PVvXt3paWlKTQ0VJKUnZ2tzMxMR//S0lLNmzdPR48elaenpzp06KBFixZpypQptXcUAACgXnB5Hhd3YB4XAADM4/Z5XAAAANyJ4AIAAIxBcAEAAMYguAAAAGMQXAAAgDEILgAAwBgEFwAAYAyCCwAAMAbBBQAAGIPgAgAAjEFwAQAAxiC4AAAAYxBcAACAMQguAADAGAQXAABgDIILAAAwBsEFAAAYg+ACAACMQXABAADGILgAAABjEFwAAIAxCC4AAMAYBBcAAGAMggsAADAGwQUAABiD4AIAAIxBcAEAAMYguAAAAGN4ursAVO6YbG7Zb3tZbtkvAABXw4gLAAAwBsEFAAAYg+ACAACMQXABAADGILgAAABjEFwAAIAxCC4AAMAYBBcAAGAMggsAADAGwQUAABiD4AIAAIxBcAEAAMYguAAAAGMQXAAAgDEILgAAwBgEFwAAYAyCCwAAMAbBBQAAGIPgAgAAjFGj4JKcnKywsDB5e3srIiJCu3btqrTvW2+9peHDhyswMFB+fn7q16+ftm7dWuOCAQBA/eVycElNTVVcXJzmz5+vjIwMDRgwQDExMcrMzKyw/wcffKDhw4crLS1N+/fv15AhQzRq1ChlZGRcc/EAAKB+sVmWZbmyQp8+fdSrVy8tX77c0RYeHq7Ro0crKSmpWtvo1q2bYmNj9etf/7pa/QsKCuTv76/8/Hz5+fm5Um61JCYm1vo2qyM+Pr7K14/JdoMqcdZeLv1IAABQoevx+e3SiEtRUZH279+v6Ohop/bo6Gjt2bOnWtsoLS3V2bNn1bx580r7FBYWqqCgwGkBAABwKbjk5uaqpKREQUFBTu1BQUE6efJktbaxePFinT9/Xvfff3+lfZKSkuTv7+9YgoODXSkTAADcpGp0ca7N5nwKw7Kscm0V2bhxoxISEpSamqqWLVtW2m/evHnKz893LMePH69JmQAA4Cbj6UrngIAAeXh4lBtdycnJKTcK81OpqamaNGmSNm3apGHDhlXZ1263y263u1IaAACoB1wacfHy8lJERITS09Od2tPT09W/f/9K19u4caMefvhhbdiwQXfddVfNKgUAAPWeSyMukjRr1iyNGzdOkZGR6tevn1asWKHMzExNnTpV0uXTPFlZWVqzZo2ky6Fl/PjxWrZsmfr27esYrfHx8ZG/v38tHgoAALjZuRxcYmNjlZeXp4ULFyo7O1vdu3dXWlqaQkNDJUnZ2dlOc7qkpKSouLhYM2bM0IwZMxztEyZM0OrVq6/9CAAAQL3hcnCRpOnTp2v69OkVvvbTMLJz586a7AIAAKAcnlUEAACMQXABAADGILgAAABjEFwAAIAxCC4AAMAYBBcAAGAMggsAADAGwQUAABiD4AIAAIxBcAEAAMYguAAAAGMQXAAAgDEILgAAwBgEFwAAYAyCCwAAMAbBBQAAGIPgAgAAjEFwAQAAxiC4AAAAYxBcAACAMQguAADAGAQXAABgDIILAAAwBsEFAAAYg+ACAACMQXABAADGILgAAABjEFwAAIAxCC4AAMAYBBcAAGAMggsAADAGwQUAABiD4AIAAIxBcAEAAMYguAAAAGMQXAAAgDEILgAAwBgEFwAAYAyCCwAAMAbBBQAAGIPgAgAAjEFwAQAAxiC4AAAAYxBcAACAMQguAADAGAQXAABgDIILAAAwBsEFAAAYo0bBJTk5WWFhYfL29lZERIR27dpVad/s7GyNHTtWnTt3VoMGDRQXF1fTWgEAQD3ncnBJTU1VXFyc5s+fr4yMDA0YMEAxMTHKzMyssH9hYaECAwM1f/58/fznP7/mggEAQP3lcnBZsmSJJk2apMmTJys8PFxLly5VcHCwli9fXmH/9u3ba9myZRo/frz8/f2vuWAAAFB/uRRcioqKtH//fkVHRzu1R0dHa8+ePbVWVGFhoQoKCpwWAAAAl4JLbm6uSkpKFBQU5NQeFBSkkydP1lpRSUlJ8vf3dyzBwcG1tm0AAGCuGl2ca7PZnL63LKtc27WYN2+e8vPzHcvx48drbdsAAMBcnq50DggIkIeHR7nRlZycnHKjMNfCbrfLbrfX2vZQuxITE9227/j4eLftGwDgfi6NuHh5eSkiIkLp6elO7enp6erfv3+tFgYAAPBTLo24SNKsWbM0btw4RUZGql+/flqxYoUyMzM1depUSZdP82RlZWnNmjWOdQ4cOCBJOnfunL7//nsdOHBAXl5e6tq1a+0cBQAAqBdcDi6xsbHKy8vTwoULlZ2dre7duystLU2hoaGSLk8499M5XW677TbH1/v379eGDRsUGhqqY8eOXVv1AACgXnE5uEjS9OnTNX369ApfW716dbk2y7JqshsAAAAnPKsIAAAYg+ACAACMQXABAADGILgAAABjEFwAAIAxCC4AAMAYBBcAAGAMggsAADAGwQUAABiD4AIAAIxBcAEAAMYguAAAAGMQXAAAgDEILgAAwBgEFwAAYAyCCwAAMAbBBQAAGIPgAgAAjEFwAQAAxiC4AAAAYxBcAACAMQguAADAGAQXAIAWLFggm82m3/3ud7W63TvvvFM2m03vv/9+rW4X9RfBBQBuAiEhIbLZbOWWRo0aqWvXrnrqqaf0/fffV7jud999pyVLligwMFAzZsxwei0vL0+vv/66fvGLX6hr167y9fWV3W5Xu3btNHr0aL399ttV1pWQkCBJmj17tkpLS2vlWN3l7NmzSkhIUI8ePdS4cWP5+/vr9ttv1+LFi1VUVOTy9q71va3MokWLnH4Gbjae7i4AAHBt8vLydPz4cUlSs2bN5OXlJUkqLi5WXl6eDh8+rMOHDys1NVV79+5VcHCw0/rz58/XxYsXtXDhQvn6+jq91qpVKxUXFzu+9/b2VsOGDZWVlaWsrCz99a9/VUxMjN588001atSoXG19+/bViBEjtHXrVq1bt07jx4+v7cO/Ib799lsNHjxYx44dkyQ1atRIhYWF2rdvn/bt26f169dr+/btatasWbW3ea3vbUW++OILJSYmunRspmHEBQAMt3//fsfXO3bs0MmTJ3Xy5Enl5ubq9OnTmjp1qiQpKytL8+fPd1o3KytL69evl5eXlyZOnFhu28XFxerdu7eSk5N15MgRXbx4UefOndPRo0c1adIkSdKWLVs0ZcqUSusr239tn4a6UUpKSjRq1CgdO3ZMrVu3Vnp6us6fP68LFy7oz3/+s5o0aaKMjAw99NBDLm23Nt7bK5WWlmrSpEm6dOmS+vXr5/JxmoLgAgCGKwsuDRs2VHh4uNNrzZo10yuvvKJu3bpJktLS0pxe/9Of/qSSkhKNHDlSzZs3L7ft999/Xx999JGmTZumn/3sZ4729u3b67XXXnN8qK5bt84x6vNTZdv+7LPPtHv37pofqJusXr1an376qSRp8+bNGjZsmCSpQYMGio2NVUpKiqTLIWP79u3V3m5tvLdXevnll7V792499NBDio6OrnYdpiG4AIDhPv74Y0lS165dHaeJrtSgQQPdfvvtki6fViopKZEkWZallStXSpLGjh1b4baHDBlS5b7LRgYkad++fRX28fLy0pgxYyRJK1asqHJ7ddEbb7wh6fJ7UdFIxgMPPKCwsDBJ0po1a6q93dp4b8scPXpU8+fPV4sWLfTSSy9VuwYTEVwAwHBlIy4///nPK+1TdvFo48aN5eHhIUk6ePCgvvvuO0nSgAEDarRvb29vx9dlgagiAwcOlCS99957NdqPu1y4cMExShQTE1NhH5vNpjvvvFOStG3btlrbd3XfW0l69NFHdf78ecdF1jczLs7FTcOdF6TFx8e7bd+o386cOaOjR49Kqjy4WJalvXv3SpJ69erlaP/ggw8kScHBwWrVqlWN9r9z507H1z169Ki0X58+fSRJOTk5+vzzz9WlS5ca7e9GO3z4sONuqO7du1far+y1kydP6vTp0xWednNVdd/bP/3pT9q+fbuGDRtm7MXPrmDEBQAMVnaaSJJ69uxZYZ+UlBRHuJkwYYKj/aOPPpJU9UhNVX744QclJSVJujxi07lz50r7durUSY0bN5YkR4i6mtWrV1d4i3d1lys/+GvqxIkTjq/btm1bab8rX7tynZqq7nublZWlOXPmyMfHx3Gtzc2OERcAMNiVweXKAFJUVKSvvvpKq1at0tKlSyVJd9xxh1NwKfuArcmphdLSUo0bN07Z2dmy2+16+eWXr7pOixYtdO7cuWp/sPv4+CgoKMjl2spUdL2Pq86ePev4uqpbkq987cp1asKV93bKlCnKz8/Xb3/7W6cLfG9mBBcAMNiVt0IHBARU2m/s2LFKSUlxXN8iyTEhXU1OazzxxBN69913JUnJycnVGrVp3ry5vv3220onwvup2NhYxcbGulyb6ar73q5bt05///vf1bNnT82aNetGluhWBBcAMFjZiEujRo3UpEkTSZcvFm3cuLFat26tPn366KGHHqrwNNKlS5ckSXa73aV9zp49W3/84x8lSS+99FKF879UxMfHx2m/Jih7T6XLF+pW5srXrlzHVdV9b3NychQXFycPDw/96U9/kqdn/fk4rz9HCgA3mYKCAn399deSLk+tP2fOHJfWb9GihaTLF/hW19NPP63FixdLkn7/+98rLi6u2uuePn3aab8maNOmjePrrKws3XrrrRX2y8rKqnAdV7jy3j7zzDPKy8vTtGnT1KVLF507d87p9SsfQVD2mpeXV62cPnM3ggsAGCojI0OWZUmSIiMjXV6/7NqWskBxNXPmzNGLL74o6fIsuLNnz3Zpf2X7qe41NampqXriiSdc2seV3nrrLfXv37/G60tSeHi4GjRooNLSUh08eLDSW6IPHjwo6fI0/jU59ebqe1t2sfXy5cu1fPnyKvuWjQA98cQTjuudTEZwAQBDlZ0mstlsTrc5V1fXrl31zjvv6Jtvvrlq39mzZztGA373u9+5PLpz9uxZ5ebmSlK52X0rc/HiRZ06dcql/VypJg8+/KlGjRopKipKu3bt0nvvvVfhcVuWpa1bt0pSjWasvdb3tr7hdmgAMFTZhbkdOnSQv7+/y+uXTQr33//+V4WFhZX2u/KD9cUXX6zRB+u+fftUWloqT09PRUVFVWudhx9+WJZl1XgZPHiwy3VWpOxOrB07djhuIb/Spk2bHOHP1XlUavre7ty5s8pjv3JuqbK2m2G0RSK4AICxykZcanKaSJKioqLk6empoqIiHThwoMI+zzzzjOODdcmSJXrqqadqtK+yD/xevXo55nMxxYQJE9SjRw9ZlqUxY8Y4nkdUWlqqTZs26dFHH5V0eWbdoUOHllv/yvlorpxbprbe2/qG4AIABjp//ry++OILSVJERESNtuHn56e77rpLkvTOO++Uez0zM9PxROcGDRrot7/9rVq1alXpUnaNRkXKtl/ZM5HqMk9PT73zzjtq3769srKyNGzYMPn6+srX11f333+/CgoKdNttt2n9+vXV3mZtvrf1Dde4AICBDhw44JiKvqbBRbo8gdlf//pXbdiwQc8995xsNpvjtbLtl319tetNfnpnS5mjR49q79698vHxMXZK+vbt2+uTTz7Riy++qLfeektHjx5Vw4YN1a1bNz344IN6/PHHXbpjp7be2/qI4AIABoqKinLcUXQtRowYoQ4dOujIkSPatWuX47oX6fKHdW3sY+3atZIuP0W5WbNm17w9d2nSpIkSExNdfi7aww8/rIcfftiprbbe28okJCQoISHhum3fnQguwHXGwx9RlzVo0EC/+c1vNHbsWC1atMgpuNSG8+fP6+WXX5bdbufnEbWCa1wAoJ574IEH1Lt3b23ZsqXCu2auxR//+Efl5ubql7/8pUJDQ2t126ifGHEBgHrOZrMpJSVFf/nLXxxzrdQWX19fJSQkuDTDLlAVggsAQD179qzweUbXaubMmbW+TdRvnCoCAADGqFFwSU5OVlhYmLy9vRUREaFdu3ZV2f+f//ynIiIi5O3trZ/97Gd69dVXa1QsAACo31w+VZSamqq4uDglJycrKipKKSkpiomJ0aFDhxQSElKu/9GjRzVy5Eg9+uijWrdunXbv3q3p06crMDBQY8aMqZWDAFAz7rrjibtLANSUyyMuS5Ys0aRJkzR58mSFh4dr6dKlCg4OrvTplK+++qpCQkK0dOlShYeHa/LkyZo4cSKzAAIAAJe5NOJSVFSk/fv3a+7cuU7t0dHR2rNnT4Xr7N27t9zTMkeMGKGVK1fqxx9/VMOGDcutU1hY6PTAr/z8fElSQUGBK+VW26VLl67Ldq/masdz9gbV8VMFqroud71fUtXvGXWVd7Wfsbr6s5+UlHSDKnE2b948t+wXuFmV/V+v1cn2LBdkZWVZkqzdu3c7tT///PPWLbfcUuE6nTp1sp5//nmntt27d1uSrBMnTlS4Tnx8vCWJhYWFhYWF5SZYjhw54krcqFKNboe+8lkWkmRZVrm2q/WvqL3MvHnzNGvWLMf3P/zwg0JDQ5WZmVmjR7dfLwUFBQoODtbx48fl5+fn7nIcqMs1dbUuqe7WRl2uoS7X1NW6pLpbW12tKz8/XyEhIWrevHmtbdOl4BIQECAPDw+dPHnSqT0nJ0dBQUEVrtOqVasK+3t6eqpFixYVrmO322W328u1+/v716l/kDJ+fn7U5QLqcl1drY26XENdrqmrdUl1t7a6WleDBrU3+4pLW/Ly8lJERITS09Od2tPT09W/f/8K1+nXr1+5/tu2bVNkZGSF17cAAABUxuUINGvWLL322mtatWqVDh8+rCeffFKZmZmaOnWqpMunea58bPnUqVP17bffatasWTp8+LBWrVqllStXavbs2bV3FAAAoF5w+RqX2NhY5eXlaeHChcrOzlb37t2VlpbmeHhWdna2MjMzHf3DwsKUlpamJ598Uq+88oratGmjP/zhDy7N4VL2VNGKTh+5E3W5hrpcV1droy7XUJdr6mpdUt2trT7VZbOs2rxHCQAA4PrhWUUAAMAYBBcAAGAMggsAADAGwQUAABijTgeXc+fOKS4uTm3atJG3t7d69uypP//5z+4uS2fPntXTTz+t6OhoBQYGymazKSEhwa01vf/++5o4caK6dOkiX19ftW3bVv/7v/+r/fv3u7WuAwcO6K677lJISIh8fHzUvHlz9evXT+vWrXNrXRV57bXXZLPZ1LhxY7fWsXPnTtlstgqXf/3rX26tTZI+/PBDjRw5Us2aNZOPj486deqk3/zmN26r5+GHH670/XL3e5aRkaHRo0erTZs2atSokbp06aKFCxfqwoULbqtJkv79739rxIgRatKkiRo3bqwhQ4Zo9+7dN7QGV36Pfvzxxxo2bJgaN26spk2b6t5779U333zj1ro+/PBDTZ48WREREbLb7bLZbDp27Nh1qam6dZWUlGjJkiW688471a5dOzVq1Ejh4eGaO3eufvjhB7fVJUl/+MMf1LdvXwUEBMhutyskJEQPPPCAPvvsM5f3WaeDy7333qs33nhD8fHx2rJli26//XY9+OCD2rBhg1vrysvL04oVK1RYWKjRo0e7tZYyy5cv17Fjx/TEE08oLS1Ny5YtU05Ojvr27av333/fbXX98MMPCg4O1gsvvKC0tDStWbNG7du317hx4/Tcc8+5ra6fysrK0uzZs9WmTRt3l+LwwgsvaO/evU5L9+7d3VrThg0bNGjQIPn7+2vNmjVKS0vTM888U7sPUHPRs88+W+592rt3rwICAtS2bVvdfvvtbqnr0KFD6t+/v44dO6alS5fq3Xff1QMPPKCFCxfqwQcfdEtNkvSf//xHAwcO1MWLF7V27VqtXbtWly5d0tChQ7V3794bVkd1f49+/vnnGjx4sIqKivR///d/WrVqlb788ksNGDBA33//vdvq2r59u/7xj38oJCSk0glYb3RdFy9eVEJCgkJDQ7V06VKlpaXp0Ucf1YoVKxQVFaWLFy+6pa6yfjExMXrttde0bds2JSYmKiMjQ3369NEXX3zh2k5r7alHtezvf/+7JcnasGGDU/vw4cOtNm3aWMXFxW6qzLJKS0ut0tJSy7Is6/vvv7ckWfHx8W6rx7Is69SpU+Xazp49awUFBVlDhw51Q0VV69OnjxUcHOzuMhzuvvtua9SoUdaECRMsX19ft9ayY8cOS5K1adMmt9bxU999953l6+trTZs2zd2lXNXOnTstSdaCBQvcVsP8+fMtSdbXX3/t1P7YY49ZkqzTp0+7pa4RI0ZYQUFB1vnz5x1tBQUFVkBAgNW/f/8bVkd1f4/ed999VkBAgJWfn+9oO3bsmNWwYUPr6aefdltdJSUljq9///vfW5Kso0eP1no9rtRVXFxs5ebmllt306ZNliRr7dq1bqmrMocOHbIkWc8++6xL+6yzIy5vv/22GjdurPvuu8+p/ZFHHtGJEyf00UcfuakyOYag65KWLVuWa2vcuLG6du2q48ePu6GiqgUEBMjTs0bP+Kx169at0z//+U8lJye7u5Q67bXXXtP58+f1zDPPuLuUq1q5cqVsNpsmTpzothrKHmny0wfDNm3aVA0aNJCXl5c7ytLu3bs1ePBgNWrUyNHWpEkTDRw4UHv27FF2dvYNqaM6v0eLi4v17rvvasyYMU7P3wkNDdWQIUP09ttvu6UuqXafvVMd1anLw8OjwmcA9u7dW5Kuy2fBtXweBgYGSpLLnwV1NrgcPHhQ4eHh5Q7o1ltvdbyOquXn5+vjjz9Wt27d3F2KSktLVVxcrO+//17JycnaunVrnfgAzMnJUVxcnBYtWqR27dq5uxwnM2bMkKenp/z8/DRixAh9+OGHbq3ngw8+UPPmzfX555+rZ8+e8vT0VMuWLTV16lQVFBS4tbYr5efn680339TQoUMVFhbmtjomTJigpk2batq0afrmm2909uxZvfvuu0pJSdGMGTPk6+vrlrqKiooqnMW0rO3TTz+90SVV6siRI7p48aLj9/6Vbr31Vn399de6dOmSGyozS9nlAnXhs6CkpESFhYX6/PPPNXnyZLVs2VKPPPKIS9uos8ElLy+vwsdgl7Xl5eXd6JKMM2PGDJ0/f17z5893dymaPn26GjZsqJYtW+rJJ5/UH/7wB02ZMsXdZWn69Onq3Lmzpk2b5u5SHPz9/fXEE08oJSVFO3bs0LJly3T8+HENHjxYW7dudVtdWVlZunDhgu677z7FxsbqH//4h+bMmaM1a9Zo5MiRbr3O5UobN27UxYsXNWnSJLfW0b59e+3du1cHDx5Uhw4d5Ofnp1GjRmnChAlatmyZ2+rq2rWr/vWvf6m0tNTRVlxc7BjFrku/W8tqqeyzwLIsnTlz5kaXZZSsrCzNnTtXkZGRuvvuu91djnx9feXt7a3w8HAdPnxYO3fuVHBwsEvbqBtj9ZWoaviprp2qqWueffZZrV+/Xi+//LIiIiLcXY5+9atfafLkycrJydHf/vY3zZw5U+fPn3frwzY3b96sv/3tb8rIyKhTP0+33XabbrvtNsf3AwYM0D333KMePXro6aef1ogRI9xSV2lpqS5duqT4+HjNnTtXkjR48GB5eXkpLi5O27dv17Bhw9xS25VWrlypFi1a6J577nFrHceOHdOoUaMUFBSkN998U4GBgfroo4/03HPP6dy5c1q5cqVb6nr88cc1adIkzZw5U/Pnz1dpaakSExP17bffSrrxp0Cqg8+Cmjl9+rTjj4rU1NQ68W+7Z88eFRUV6ciRI3rppZc0ZMgQbd++3aXRIPcfRSVatGhRYfI/ffq0pIoTOC5LTEzUc889p+eff14zZ850dzmSpJCQEEVGRmrkyJFavny5HnvsMc2bN++63BVQHefOndOMGTP0+OOPq02bNvrhhx/0ww8/qKioSNLlu6HOnz/vltoq0rRpU91999365JNPrsudAdVRdu78p8EpJiZG0uVbVt3tk08+0b59+/SLX/zC7Q+bmzt3rgoKCrR161aNGTNGAwcO1Jw5c7R06VKtWrVK//znP91S18SJE7Vo0SKtXbtW7dq1U0hIiA4dOuT4I6Jt27ZuqasiZT9zlX0W2Gw2NW3a9AZXZYYzZ85o+PDhysrKUnp6un72s5+5uyRJUq9evdS3b1899NBD2rFjhyzL0q9+9SuXtlFng0uPHj10+PBhFRcXO7WXnX91922hdVViYqISEhKUkJDg8g/DjdS7d28VFxdft7kYriY3N1enTp3S4sWL1axZM8eyceNGnT9/Xs2aNdNDDz3kltoqU3Yqxl1/YVZ0nYH0/+qqC3/NlY1iTJ482c2VXJ7DqGvXruWuZSm7Pdud1+k988wzys3N1aeffqpjx45pz549OnPmjHx9fevECG2ZDh06yMfHp8Lrbj799FN17NhR3t7ebqisbjtz5oyGDRumo0ePKj09vdL/u+7WpEkTdenSRV9++aVL67n/N00l7rnnHp07d06bN292an/jjTfUpk0b9enTx02V1V2/+c1vlJCQoAULFig+Pt7d5VRpx44datCggdv+CmjVqpV27NhRbhkxYoS8vb21Y8eOOjXPzJkzZ/Tuu++qZ8+ebvtFPWbMGEnSli1bnNrT0tIkSX379r3hNV2psLBQ69atU+/evevEHzZt2rTRZ599pnPnzjm1l82V4u6Lwe12u7p3767Q0FBlZmYqNTVVjz76qHx8fNxa15U8PT01atQovfXWWzp79qyjPTMzUzt27NC9997rxurqprLQ8s0332jbtm1Op53rmrLw3LFjR5fWq7PXuMTExGj48OGaNm2aCgoK1LFjR23cuFHvvfee1q1bJw8PD7fWt2XLFp0/f97xn+nQoUN68803JUkjR450utXwRli8eLF+/etf684779Rdd91VbrZQd32oPPbYY/Lz81Pv3r0VFBSk3Nxcbdq0SampqZozZ47jdrgbzdvbW4MHDy7Xvnr1anl4eFT42o0yduxYx6m1gIAAffXVV1q8eLFOnTql1atXu62u6OhojRo1SgsXLlRpaan69u2rffv2KTExUXfffbf+53/+x221SdJf/vIXnT59uk6MtkhSXFycRo8ereHDh+vJJ59UQECA/vWvfykpKUldu3Z1nGK70Q4ePKjNmzcrMjJSdrtd//3vf7Vo0SK3zIBcnd+jiYmJuv3223X33Xdr7ty5unTpkn79618rICBATz31lNvq+v777x2n+8pGhLZs2aLAwEAFBgZq0KBBN7wum82mESNGKCMjQ0uXLlVxcbHTZ0FgYKA6dOhww+v68ccfNXz4cI0dO1adOnWSj4+PvvzySy1btkyFhYWu/6Ht0qwvN9jZs2etX/7yl1arVq0sLy8v69Zbb7U2btzo7rIsy7Ks0NBQS1KFy/WchKgygwYNqrQed/4zr1q1yhowYIAVEBBgeXp6Wk2bNrUGDRp0XSZCqg11YQK6pKQkq2fPnpa/v7/l4eFhBQYGWvfcc4/173//2611WZZlXbhwwXrmmWes4OBgy9PT0woJCbHmzZtnXbp0yd2lWcOHD7d8fX2tgoICd5fi8P7771vR0dFWq1atLB8fH+uWW26xnnrqqQonCbtRvvjiC2vgwIFW8+bNLS8vL6tjx47WggULrHPnzt3wWqr7e3Tfvn3W0KFDrUaNGll+fn7W6NGjy03sd6PrKpsosqJl0KBBbqnr6NGjVX4OTJgwwS11Xbp0yZo8ebIVHh5uNW7c2PL09LTatWtn/eIXv7A+++wzl/dns6w6cg8jAADAVdTZa1wAAAB+iuACAACMQXABAADGILgAAABjEFwAAIAxCC4AAMAYBBcAAGAMggsAADAGwQUAABiD4AIAAIxBcAEAAMb4/wCJ8Zywven0JgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(1,X))\n",
    "x2 = X\n",
    "x3 = list(np.arange(X+1,Y+10))\n",
    "plt.bar(x1, geom.pmf(x1, p=p), color ='gray')\n",
    "plt.bar(x2, geom.pmf(x2, p=p), color ='#DFFF00')\n",
    "plt.bar(x3, geom.pmf(x3, p=p), color ='gray')\n",
    "plt.xlim(0,10)\n",
    "plt.xticks(np.arange(0,Y+10), fontsize=12, ha='center')\n",
    "plt.title(f'G({p})')\n",
    "prob = np.sum([geom.pmf(x2, p=p)])\n",
    "plt.text(8.5, 0.02, f'$P({np.round(X, 3)}) = $ {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wHfxrvvOyRiq"
   },
   "source": [
    "$P(X>s+t\\ |\\ X>s) = P(X>t)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Bl35Ww-5HNtN"
   },
   "source": [
    "<a name='Poisson_Distribution'></a>\n",
    "\n",
    "## **2.5. Poisson Distribution:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Yv5EDsRSZbJO"
   },
   "source": [
    "$P(X=x) = \\frac{e^{-\\lambda}\\lambda^x}{x!} \\quad \\quad x = 0,1,...,\\infty$\n",
    "\n",
    "$\\\\ $\n",
    "\n",
    "$E(X) = \\lambda$\n",
    "\n",
    "$Var(X) = \\lambda$\n",
    "\n",
    "$Skewness(X) = \\lambda^{-\\frac{1}{2}}$\n",
    "\n",
    "$Kurtosis(X) = \\lambda^{-1}$\n",
    "\n",
    "$Mode(X) = \\begin{cases}\\lambda,\\lambda-1 & \\lambda \\in integer \\\\ [\\lambda] & \\lambda \\not\\in integer \\end{cases}$\n",
    "\n",
    "$\\\\ $\n",
    "\n",
    "Moment-generating function:\n",
    "\n",
    "$M_{x}(t) = e^{\\lambda(e^t-1)}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 281
    },
    "id": "f1pJM57IHM9n",
    "outputId": "d9c61aba-d771-41b4-f4ed-3f187c2f59ad"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "N = 1000000\n",
    "lam = 3\n",
    "\n",
    "poi_data = np.random.poisson(lam = lam, size = N)\n",
    "\n",
    "sns.histplot(poi_data, color='Brown', stat='density', bins=50)\n",
    "\n",
    "plt.title('Poisson Distribution');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "id": "rSZc3xTyXLcW"
   },
   "outputs": [],
   "source": [
    "def mode_poisson(lam):\n",
    "  if math.modf(lam)[0] == 0.0:\n",
    "    return [lam, lam-1]\n",
    "  else:\n",
    "    return np.floor(lam)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "NVaPuaB8dKs3",
    "outputId": "68a9fe60-8862-47f8-ab2c-e67d6b90c41f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the P(3) Distribution is:  3.0\n",
      "The median of the P(3) Distribution is:  3.0\n",
      "The variance of the P(3) Distribution is:  3.0\n",
      "The standard deviation of the P(3) Distribution is:  1.7321\n",
      "The mode of the P(3) Distribution is:  [3 2]\n",
      "The skewness of the P(3) Distribution is:  0.5774\n",
      "The kurtosis of the P(3) Distribution is:  0.3333\n"
     ]
    }
   ],
   "source": [
    "lam = 3\n",
    "print(f'The mean of the P({lam}) Distribution is: ', np.round(poisson.mean(lam), 4))\n",
    "print(f'The median of the P({lam}) Distribution is: ', np.round(poisson.median(lam), 4))\n",
    "print(f'The variance of the P({lam}) Distribution is: ', np.round(poisson.var(lam), 4))\n",
    "print(f'The standard deviation of the P({lam}) Distribution is: ', np.round(poisson.std(lam), 4))\n",
    "print(f'The mode of the P({lam}) Distribution is: ', np.round(mode_poisson(lam), 4))\n",
    "print(f'The skewness of the P({lam}) Distribution is: ', np.round(poisson.stats(lam, moments='mvsk')[2], 4))\n",
    "print(f'The kurtosis of the P({lam}) Distribution is: ', np.round(poisson.stats(lam, moments='mvsk')[3], 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tuMbDMELNsM6"
   },
   "source": [
    "Integrating the PDF, gives us the cumulative distribution function (CDF) which is a function that maps values to their percentile rank in a distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "id": "SYtrA-ETNhhd",
    "outputId": "ab9870f5-c7fe-4cae-cdd1-b9ab0aa4e7c2"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 8\n",
    "x = np.arange(0, n, 0.001)\n",
    "x1 = np.arange(0, n)\n",
    "x2 = np.arange(0, n-1) + 0.999\n",
    "\n",
    "plt.scatter(x, poisson.cdf(x, lam), color = 'r')\n",
    "plt.scatter(x2, poisson.cdf(x2, lam), color = 'white', edgecolor='black', s=100)\n",
    "plt.scatter(x1, poisson.cdf(x1, lam), color = 'black', edgecolor='black', s=100)\n",
    "plt.xlim(-0.1,n);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "SJ5RowUaeXoj"
   },
   "source": [
    "The poisson distribution histogram depends on the $\\lambda$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 356
    },
    "id": "Oca3B_SaedDi",
    "outputId": "8774d02f-6c9f-4c88-ae6b-af1f03a8e0e7"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lam1, lam2, lam3 = [3, 4, 10]\n",
    "\n",
    "fig, axes = plt.subplots(1, 3, figsize=(15, 5), sharey=True)\n",
    "fig.suptitle('Poisson Distribution')\n",
    "\n",
    "sns.histplot(ax=axes[0], x=np.random.poisson(lam = lam1, size = N),  bins=50, color = '#B4EA1A')\n",
    "axes[0].set_title(f'P({lam1})')\n",
    "\n",
    "sns.histplot(ax=axes[1], x=np.random.poisson(lam = lam2, size = N),  bins=50, color = '#6960EC')\n",
    "axes[1].set_title(f'P({lam2})')\n",
    "\n",
    "sns.histplot(ax=axes[2], x=np.random.poisson(lam = lam3, size = N),  bins=50, color = '#F75D59')\n",
    "axes[2].set_title(f'P({lam3})');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fndQ_A7BgO83"
   },
   "source": [
    "To find the left probability of a point use the code below:\n",
    "\n",
    "''\n",
    "poisson.cdf($\\lambda$)\n",
    "''\n",
    "\n",
    "To find the right probability of a point use the code below:\n",
    "\n",
    "''\n",
    "poisson.sf($\\lambda$)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "7ZIdi46ggO85",
    "outputId": "d470add7-da35-4c3c-e91f-2f7c7583b229"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The left probability of *3* in the P(3) Distribution is:  0.6472318887822313\n",
      "The Right probability of *3* in the P(3) Distribution is:  0.3527681112177687\n"
     ]
    }
   ],
   "source": [
    "X = 3\n",
    "lam = 3\n",
    "print(f'The left probability of *{X}* in the P({lam}) Distribution is: ', poisson.cdf(X, lam))\n",
    "print(f'The Right probability of *{X}* in the P({lam}) Distribution is: ', poisson.sf(X, lam))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hqGdGmQVFws-"
   },
   "source": [
    "To find the probability between two points $[X,Y]$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Q5VYhhDBFws-",
    "outputId": "fc083bb0-b61c-45d1-e009-04820d814c15"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *[2, 5]* in the P(3) Distribution is:  0.716933784497241\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "Y = 5\n",
    "lam = 3\n",
    "xs = np.arange(X, Y+1)\n",
    "print(f'The probability between *[{X}, {Y}]* in the P({lam}) Distribution is: ', np.sum([poisson.pmf(xs, lam) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "id": "k_b3ct93GOio",
    "outputId": "1d247b32-7278-45b0-a76a-8c3370bb51d2"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X))\n",
    "x2 = list(np.arange(X,Y+1))\n",
    "x3 = list(np.arange(Y+1,Y+10))\n",
    "plt.bar(x1, poisson.pmf(x1, lam), color ='gray')\n",
    "plt.bar(x2, poisson.pmf(x2, lam), color ='#DFFF00')\n",
    "plt.bar(x3, poisson.pmf(x3, lam), color ='gray')\n",
    "plt.xlim(-1,Y+10)\n",
    "plt.xticks(np.arange(0,Y+10), fontsize=12, ha='center')\n",
    "plt.title(f'$P\\ (\\lambda = {lam})$')\n",
    "xs = np.arange(X, Y+1)\n",
    "prob = np.sum([poisson.pmf(xs, lam) for xs in xs])\n",
    "plt.text(9, 0.02, f'$P({np.round(X, 3)} \\leq X \\leq {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "GAvzrWPEGo1l"
   },
   "source": [
    "To find the probability between two points $(X,Y)$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "e9iBud3qGo1l",
    "outputId": "17d65f0d-df3c-4c0f-b315-b0ae3ec543f5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *(2, 5)* in the P(3) Distribution is:  0.3920731633969286\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "Y = 5\n",
    "lam = 3\n",
    "xs = np.arange(X+1, Y)\n",
    "print(f'The probability between *({X}, {Y})* in the P({lam1}) Distribution is: ', np.sum([poisson.pmf(xs, lam) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "id": "0yfJR2TGGo1m",
    "outputId": "25ea5192-ac1c-41a3-815e-7e72fcf6d3fb"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X+1))\n",
    "x2 = list(np.arange(X+1,Y))\n",
    "x3 = list(np.arange(Y,Y+10))\n",
    "plt.bar(x1, poisson.pmf(x1, lam), color ='gray')\n",
    "plt.bar(x2, poisson.pmf(x2, lam), color ='#DFFF00')\n",
    "plt.bar(x3, poisson.pmf(x3, lam), color ='gray')\n",
    "plt.xlim(-1,Y+10)\n",
    "plt.xticks(np.arange(0,Y+10), fontsize=12, ha='center')\n",
    "plt.title(f'$P\\ (\\lambda = {lam})$')\n",
    "xs = np.arange(X+1, Y)\n",
    "prob = np.sum([poisson.pmf(xs, lam) for xs in xs])\n",
    "plt.text(9, 0.02, f'$P({np.round(X, 3)} < X < {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yxIp1f3HHI0o"
   },
   "source": [
    "To find the probability between two points $[X,Y)$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "IqrF0QKUHI0p",
    "outputId": "58c1953f-7e31-4052-e818-21d9e1390c50"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *[2, 5)* in the P(3) Distribution is:  0.6161149710523164\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "Y = 5\n",
    "lam = 3\n",
    "xs = np.arange(X, Y)\n",
    "print(f'The probability between *[{X}, {Y})* in the P({lam1}) Distribution is: ', np.sum([poisson.pmf(xs, lam) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "id": "CDe7D1R2HI0p",
    "outputId": "66310c4b-9a14-45eb-afab-cebe2586b636"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X))\n",
    "x2 = list(np.arange(X,Y))\n",
    "x3 = list(np.arange(Y,Y+10))\n",
    "plt.bar(x1, poisson.pmf(x1, lam), color ='gray')\n",
    "plt.bar(x2, poisson.pmf(x2, lam), color ='#DFFF00')\n",
    "plt.bar(x3, poisson.pmf(x3, lam), color ='gray')\n",
    "plt.xlim(-1,Y+10)\n",
    "plt.xticks(np.arange(0,Y+10), fontsize=12, ha='center')\n",
    "plt.title(f'$P\\ (\\lambda = {lam})$')\n",
    "xs = np.arange(X, Y)\n",
    "prob = np.sum([poisson.pmf(xs, lam) for xs in xs])\n",
    "plt.text(9, 0.02, f'$P({np.round(X, 3)} \\leq X < {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9-xTzF_IHvA3"
   },
   "source": [
    "To find the probability between two points $(X,Y]$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "mgkimrDrHvA3",
    "outputId": "e5be5ea8-8a6f-4ed9-e3d2-c3c3c2147052"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *(2, 5]* in the P(3) Distribution is:  0.49289197684185315\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "Y = 5\n",
    "lam = 3\n",
    "xs = np.arange(X+1, Y+1)\n",
    "print(f'The probability between *({X}, {Y}]* in the P({lam1}) Distribution is: ', np.sum([poisson.pmf(xs, lam) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "id": "IZpr3BEHHvA4",
    "outputId": "7db54a1d-e658-4cdf-f434-fe2e2230ba5e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X+1))\n",
    "x2 = list(np.arange(X+1,Y+1))\n",
    "x3 = list(np.arange(Y+1,Y+10))\n",
    "plt.bar(x1, poisson.pmf(x1, lam), color ='gray')\n",
    "plt.bar(x2, poisson.pmf(x2, lam), color ='#DFFF00')\n",
    "plt.bar(x3, poisson.pmf(x3, lam), color ='gray')\n",
    "plt.xlim(-1,Y+10)\n",
    "plt.xticks(np.arange(0,Y+10), fontsize=12, ha='center')\n",
    "plt.title(f'$P\\ (\\lambda = {lam})$')\n",
    "xs = np.arange(X+1, Y+1)\n",
    "prob = np.sum([poisson.pmf(xs, lam) for xs in xs])\n",
    "plt.text(9, 0.02, f'$P({np.round(X, 3)} < X \\leq {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ew39Mly0IJSg"
   },
   "source": [
    "To find the probability of a point use the code below:\n",
    "\n",
    "''\n",
    "poisson.pmf($X, \\lambda$)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "iupFftiIIJSg",
    "outputId": "7420ee3a-10ec-4e5e-e27c-6da8ff9338a1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of *X=2* in the P(3) Distribution is:  0.22404180765538775\n"
     ]
    }
   ],
   "source": [
    "X = 2\n",
    "lam = 3\n",
    "print(f'The probability of *X={X}* in the P({lam}) Distribution is: ', poisson.pmf(X, lam))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "id": "FVdZwFXTIJSg",
    "outputId": "9c469f7b-0ec1-4257-adc9-d050df69c6b6"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X))\n",
    "x2 = X\n",
    "x3 = list(np.arange(X+1,Y+10))\n",
    "plt.bar(x1, poisson.pmf(x1, lam), color ='gray')\n",
    "plt.bar(x2, poisson.pmf(x2, lam), color ='#DFFF00')\n",
    "plt.bar(x3, poisson.pmf(x3, lam), color ='gray')\n",
    "plt.xlim(-1,Y+10)\n",
    "plt.xticks(np.arange(0,Y+10), fontsize=12, ha='center')\n",
    "plt.title(f'$P\\ (\\lambda = {lam})$')\n",
    "prob = poisson.pmf(x2, lam)\n",
    "plt.text(9, 0.02, f'$P({np.round(X, 3)}) = $ {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dtrIR0AZhZla"
   },
   "source": [
    "<a name='Discrete_Uniform_Distribution'></a>\n",
    "\n",
    "## **2.6. Discrete Uniform Distribution:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "faSLp_qDiCBl"
   },
   "source": [
    "$P(X=x) = \\frac{1}{n} \\quad \\quad x = a,a+1,...,b-1,b$\n",
    "\n",
    "$\\ \\qquad \\qquad \\qquad \\qquad n = b − a + 1$\n",
    "\n",
    "$\\\\ $\n",
    "\n",
    "$E(X) = \\frac{a+b}{2}$\n",
    "\n",
    "$Var(X) = \\frac{n^2-1}{12}$\n",
    "\n",
    "$Median(X) = \\frac{a+b}{2}$\n",
    "\n",
    "$Skewness(X) = 0$\n",
    "\n",
    "$Kurtosis(X) = -\\frac{6(n^2+1)}{5(n^2-1)}$\n",
    "\n",
    "$\\\\ $\n",
    "\n",
    "Moment-generating function:\n",
    "\n",
    "$M_{x}(t) = \\frac{e^{at}-e^{(b+1)t}}{n(1-e^t)}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 284
    },
    "id": "LRJzFFArhfGC",
    "outputId": "219028fc-6ded-40e4-91cc-8cf3aacef0c7"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "N = 1000000\n",
    "a, b = [2,5]\n",
    "\n",
    "ud_data = np.random.randint(low = a, high = b+1, size = N)\n",
    "\n",
    "sns.histplot(ud_data, color='Silver', stat='density', bins=50)\n",
    "\n",
    "plt.xticks(list(range(a,b+1)), fontsize=12, ha='center')\n",
    "plt.title('Discrete Uniform Distribution');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "3WutY8pHnY9x",
    "outputId": "edab00b6-2de4-4c14-f16e-93c80cb5a19f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the U[2 3 4 5] Distribution is:  3.5\n",
      "The median of the U[2 3 4 5] Distribution is:  3.0\n",
      "The variance of the U[2 3 4 5] Distribution is:  1.25\n",
      "The standard deviation of the U[2 3 4 5] Distribution is:  1.118\n",
      "The skewness of the U[2 3 4 5] Distribution is:  0.0\n",
      "The kurtosis of the U[2 3 4 5] Distribution is:  -1.36\n"
     ]
    }
   ],
   "source": [
    "a, b = [2,5]\n",
    "r = np.arange(a, b+1)\n",
    "print(f'The mean of the U{r} Distribution is: ', np.round(randint.mean(a, b+1), 4))\n",
    "print(f'The median of the U{r} Distribution is: ', np.round(randint.median(a, b+1), 4))\n",
    "print(f'The variance of the U{r} Distribution is: ', np.round(randint.var(a, b+1), 4))\n",
    "print(f'The standard deviation of the U{r} Distribution is: ', np.round(randint.std(a, b+1), 4))\n",
    "print(f'The skewness of the U{r} Distribution is: ', np.round(randint.stats(a, b+1, moments='mvsk')[2], 4))\n",
    "print(f'The kurtosis of the U{r} Distribution is: ', np.round(randint.stats(a, b+1, moments='mvsk')[3], 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "CvfsH5z3qgnM"
   },
   "source": [
    "Integrating the PDF, gives us the cumulative distribution function (CDF) which is a function that maps values to their percentile rank in a distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "id": "zyRpPYEHqgnU",
    "outputId": "43ef8ddc-ac4a-48f5-f8ba-3b79a173da26"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 6\n",
    "x = np.arange(a-2, b+1, 0.001)\n",
    "x1 = np.arange(a-2, b+1)\n",
    "x2 = np.arange(a-2, b) + 0.999\n",
    "\n",
    "plt.scatter(x, randint.cdf(x, a, b+1), color = 'r')\n",
    "plt.scatter(x2, randint.cdf(x2, a, b+1), color = 'white', edgecolor='black', s=100)\n",
    "plt.scatter(x1, randint.cdf(x1, a, b+1), color = 'black', edgecolor='black', s=100)\n",
    "plt.xlim(1,n);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yP7AtGPYr4nI"
   },
   "source": [
    "To find the left probability of a point use the code below:\n",
    "\n",
    "''\n",
    "randint.cdf($a, b$)\n",
    "''\n",
    "\n",
    "To find the right probability of a point use the code below:\n",
    "\n",
    "''\n",
    "randint.sf($a, b$)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "YvF4qfAQr4nJ",
    "outputId": "64337939-00e8-4d17-994e-2379a41a7cf8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The left probability of *4* in the U[2 3 4 5] Distribution is:  0.75\n",
      "The Right probability of *4* in the U[2 3 4 5] Distribution is:  0.25\n"
     ]
    }
   ],
   "source": [
    "X = 4\n",
    "a, b = [2,5]\n",
    "r = np.arange(a, b+1)\n",
    "print(f'The left probability of *{X}* in the U{r} Distribution is: ', randint.cdf(X, a, b+1))\n",
    "print(f'The Right probability of *{X}* in the U{r} Distribution is: ', randint.sf(X, a, b+1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FDJNw20esgdN"
   },
   "source": [
    "To find the probability between two points $[X,Y]$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "o-kvkIDwsgdN",
    "outputId": "7b9f9df3-2cdb-4c62-bf87-7a3cac22f69a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *[3, 5]* in the U[2, 3, 4, 5] Distribution is:  0.75\n"
     ]
    }
   ],
   "source": [
    "X = 3\n",
    "Y = 5\n",
    "a, b = [2,5]\n",
    "r = list(np.arange(a, b+1))\n",
    "xs = np.arange(X, Y+1)\n",
    "print(f'The probability between *[{X}, {Y}]* in the U{r} Distribution is: ', np.sum([randint.pmf(xs, a, b+1) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "id": "yP01JTvYsgdO",
    "outputId": "24c436fc-b75a-47c3-9b81-ea19470dfdc7"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X))\n",
    "x2 = list(np.arange(X,Y+1))\n",
    "x3 = list(np.arange(Y+1,Y+10))\n",
    "plt.bar(x1, randint.pmf(x1, a, b+1), color ='gray')\n",
    "plt.bar(x2, randint.pmf(x2, a, b+1), color ='#DFFF00')\n",
    "plt.bar(x3, randint.pmf(x3, a, b+1), color ='gray')\n",
    "plt.xlim(a-1,b+2)\n",
    "plt.xticks(np.arange(a-1,b+2), fontsize=12, ha='center')\n",
    "plt.title(f'$U\\ {r}$')\n",
    "xs = np.arange(X, Y+1)\n",
    "prob = np.sum([randint.pmf(xs, a, b+1) for xs in xs])\n",
    "plt.text(7, 0.02, f'$P({np.round(X, 3)} \\leq X \\leq {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OEUvv9Xttzvx"
   },
   "source": [
    "To find the probability between two points $(X,Y)$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "1BLkLtJEtzvy",
    "outputId": "fb81075a-0db3-4946-c57b-f7dc40d2b243"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *(3, 5)* in the U[2, 3, 4, 5] Distribution is:  0.25\n"
     ]
    }
   ],
   "source": [
    "X = 3\n",
    "Y = 5\n",
    "a, b = [2,5]\n",
    "r = list(np.arange(a, b+1))\n",
    "xs = np.arange(X+1, Y)\n",
    "print(f'The probability between *({X}, {Y})* in the U{r} Distribution is: ', np.sum([randint.pmf(xs, a, b+1) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "id": "ESYmvv4dtzvz",
    "outputId": "f53e941a-2a3a-46d1-8562-cf3193fbdb07"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X+1))\n",
    "x2 = list(np.arange(X+1,Y))\n",
    "x3 = list(np.arange(Y,Y+10))\n",
    "plt.bar(x1, randint.pmf(x1, a, b+1), color ='gray')\n",
    "plt.bar(x2, randint.pmf(x2, a, b+1), color ='#DFFF00')\n",
    "plt.bar(x3, randint.pmf(x3, a, b+1), color ='gray')\n",
    "plt.xlim(a-1,b+2)\n",
    "plt.xticks(np.arange(a-1,b+2), fontsize=12, ha='center')\n",
    "plt.title(f'$U\\ {r}$')\n",
    "xs = np.arange(X+1, Y)\n",
    "prob = np.sum([randint.pmf(xs, a, b+1) for xs in xs])\n",
    "plt.text(7, 0.02, f'$P({np.round(X, 3)} < X < {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "my_4el6yuxfx"
   },
   "source": [
    "To find the probability between two points $[X,Y)$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "trGE9TJauxfy",
    "outputId": "814f19c5-f407-4248-d441-96eba7e07504"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *[3, 5)* in the U[2, 3, 4, 5] Distribution is:  0.5\n"
     ]
    }
   ],
   "source": [
    "X = 3\n",
    "Y = 5\n",
    "a, b = [2,5]\n",
    "r = list(np.arange(a, b+1))\n",
    "xs = np.arange(X, Y)\n",
    "print(f'The probability between *[{X}, {Y})* in the U{r} Distribution is: ', np.sum([randint.pmf(xs, a, b+1) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "id": "ubM8k-W8uxfz",
    "outputId": "76f861ac-77d1-45e8-c172-0bcdaabc26e4"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BJdqDg4P1xRdfVGiMwsJCXbx4UXXq1LG0xcXFlRqzf//+Nx0zLy9P2dnZJTYAAADgZqwKvxkZGSooKJCPj0+Jdh8fH6WlpVVojAULFig3N1cjR460tKWlpVk95rx58+Tp6WnZfH19rbgSAAAAGJFNH3gzmUr+CtRsNpdqK0tMTIwiIyMVGxur+vXrV2rM8PBwZWVlWbbk5GQrrgAAAABG5GRNZ29vbzk6OpaakU1PTy81c3uj2NhYTZgwQZs2bVLfvn1L7GvQoIHVY7q6usrV1dWa8gEAAGBwVs38uri4yN/fX/v27SvRvm/fPvXo0aPc42JiYvTkk09q48aNGjx4cKn9gYGBpcb87LPPbjomAAAAYC2rZn4ladq0aQoJCVHXrl0VGBio1atXKykpSZMnT5ZUtBwhJSVFa9eulVQUfMeNG6d3331XAQEBlhneGjVqyNPTU5I0depU9erVS2+++aYeffRRbd++Xfv379exY8eq6joBAAAA69f8jho1SosXL9acOXPUuXNnHTlyRLt27VKzZs0kSampqSXu+btq1Spdu3ZNU6ZMUcOGDS3b1KlTLX169OihTz75RB999JHuv/9+RUdHKzY2Vg8++GAVXCIAAABQxOqZX0kKDQ1VaGhomfuio6NLvD506FCFxhwxYoRGjBhhSzkAAABAhdh0twcAAADAHhF+AQAAYBiEXwAAABgG4RcAAACGQfgFAACAYRB+AQAAYBiEXwAAABgG4RcAAACGQfgFAACAYRB+AQAAYBiEXwAAABgG4RcAAACGQfgFAACAYRB+AQAAYBiEXwAAABgG4RcAAACGQfgFAACAYRB+AQAAYBiEXwAAABgG4RcAAACGQfgFAACAYRB+AQAAYBiEXwAAABgG4RcAAACGQfgFAACAYRB+AQAAYBiEXwAAABgG4RcAAACGQfgFAACAYRB+AQAAYBiEXwAAABgG4RcAAACGQfgFAACAYRB+AQAAYBiEXwAAABgG4RcAAACGQfgFAACAYRB+AQAAYBiEXwAAABgG4RcAAACGQfgFAACAYRB+AQAAYBiEXwAAABgG4RcAAACGQfgFAACAYRB+AQAAYBiEXwAAABgG4RcAAACGQfgFAACAYRB+AQAAYBiEXwAAABgG4RcAAACGQfgFAACAYRB+AQAAYBiEXwAAABgG4RcAAACGQfgFAACAYRB+AQAAYBiEXwAAABiGTeF3+fLlatGihdzc3OTv76+jR4+W2zc1NVVjxoxRmzZt5ODgoLCwsFJ9oqOjZTKZSm1XrlyxpTwAAACgTFaH39jYWIWFhWnWrFlKSEhQUFCQBg4cqKSkpDL75+XlqV69epo1a5Y6depU7rgeHh5KTU0tsbm5uVlbHgAAAFAuq8PvwoULNWHCBE2cOFHt2rXT4sWL5evrqxUrVpTZv3nz5nr33Xc1btw4eXp6ljuuyWRSgwYNSmwAAABAVbIq/Obn5ys+Pl7BwcEl2oODg/XFF19UqpCcnBw1a9ZMTZo00ZAhQ5SQkHDT/nl5ecrOzi6xAQAAADdjVfjNyMhQQUGBfHx8SrT7+PgoLS3N5iLatm2r6Oho7dixQzExMXJzc1PPnj11+vTpco+ZN2+ePD09LZuvr6/N5wcAAIAx2PSBN5PJVOK12Wwu1WaNgIAAPfHEE+rUqZOCgoL0t7/9Tffdd5+WLl1a7jHh4eHKysqybMnJyTafHwAAAMbgZE1nb29vOTo6lprlTU9PLzUbXBkODg7q1q3bTWd+XV1d5erqWmXnBAAAwN3PqplfFxcX+fv7a9++fSXa9+3bpx49elRZUWazWYmJiWrYsGGVjQkAAABYNfMrSdOmTVNISIi6du2qwMBArV69WklJSZo8ebKkouUIKSkpWrt2reWYxMRESUUfajt37pwSExPl4uIiPz8/SVJUVJQCAgLUunVrZWdna8mSJUpMTNSyZcuq4BIBAACAIlaH31GjRun8+fOaM2eOUlNT1aFDB+3atUvNmjWTVPRQixvv+dulSxfL1/Hx8dq4caOaNWums2fPSpIyMzM1adIkpaWlydPTU126dNGRI0fUvXv3SlwaAAAAUJLV4VeSQkNDFRoaWua+6OjoUm1ms/mm4y1atEiLFi2ypRQAAACgwmy62wMAAABgjwi/AAAAMAzCLwAAAAyD8AsAAADDIPwCAADAMAi/AAAAMAzCLwAAAAyD8AsAAADDIPwCAADAMAi/AAAAMAzCLwAAAAyD8AsAAADDIPwCAADAMAi/AAAAMAzCLwAAAAyD8AsAAADDIPwCAADAMAi/AAAAMAzCLwAAAAyD8AsAAADDIPwCAADAMAi/AAAAMAzCLwAAAAyD8AsAAADDIPwCAADAMAi/AAAAMAzCLwAAAAyD8AsAAADDIPwCAADAMAi/AAAAMAzCLwAAAAyD8AsAAADDIPwCAADAMAi/AAAAMAzCLwAAAAyD8AsAAADDIPwCAADAMAi/AAAAMAzCLwAAAAyD8AsAAADDIPwCAADAMAi/AAAAMAzCLwAAAAyD8AsAAADDIPwCAADAMAi/AAAAMAzCLwAAAAyD8AsAAADDIPwCAADAMAi/AAAAMAzCLwAAAAyD8AsAAADDIPwCAADAMAi/AAAAMAzCLwAAAAyD8AsAAADDIPwCAADAMAi/AAAAMAzCLwAAAAyD8AsAAADDsCn8Ll++XC1atJCbm5v8/f119OjRcvumpqZqzJgxatOmjRwcHBQWFlZmvy1btsjPz0+urq7y8/PTtm3bbCkNAAAAKJfV4Tc2NlZhYWGaNWuWEhISFBQUpIEDByopKanM/nl5eapXr55mzZqlTp06ldknLi5Oo0aNUkhIiE6ePKmQkBCNHDlSX331lbXlAQAAAOWyOvwuXLhQEyZM0MSJE9WuXTstXrxYvr6+WrFiRZn9mzdvrnfffVfjxo2Tp6dnmX0WL16sfv36KTw8XG3btlV4eLj+8Ic/aPHixeXWkZeXp+zs7BIbAAAAcDNWhd/8/HzFx8crODi4RHtwcLC++OILm4uIi4srNWb//v1vOua8efPk6elp2Xx9fW0+PwAAAIzBqvCbkZGhgoIC+fj4lGj38fFRWlqazUWkpaVZPWZ4eLiysrIsW3Jyss3nBwAAgDE42XKQyWQq8dpsNpdq+73HdHV1laura6XOCQAAAGOxaubX29tbjo6OpWZk09PTS83cWqNBgwZVPiYAAABwI6vCr4uLi/z9/bVv374S7fv27VOPHj1sLiIwMLDUmJ999lmlxgQAAABuZPWyh2nTpikkJERdu3ZVYGCgVq9eraSkJE2ePFlS0VrclJQUrV271nJMYmKiJCknJ0fnzp1TYmKiXFxc5OfnJ0maOnWqevXqpTfffFOPPvqotm/frv379+vYsWNVcIkAAABAEavD76hRo3T+/HnNmTNHqamp6tChg3bt2qVmzZpJKnqoxY33/O3SpYvl6/j4eG3cuFHNmjXT2bNnJUk9evTQJ598otmzZ+uvf/2r7r33XsXGxurBBx+sxKUBAAAAJdn0gbfQ0FCFhoaWuS86OrpUm9lsvuWYI0aM0IgRI2wpBwAAAKgQmx5vDAAAANgjwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAw7Ap/C5fvlwtWrSQm5ub/P39dfTo0Zv2P3z4sPz9/eXm5qaWLVtq5cqVJfZHR0fLZDKV2q5cuWJLeQAAwOBmz54tk8mkt956q7pLQRUZMGCATCaTPv/880qNY3X4jY2NVVhYmGbNmqWEhAQFBQVp4MCBSkpKKrP/mTNnNGjQIAUFBSkhIUEzZ87UCy+8oC1btpTo5+HhodTU1BKbm5ubbVcFAADsWtOmTcucGKtZs6b8/Pz0l7/8RefOnSvz2J9//lkLFy5UvXr1NGXKlBL7Tpw4oaioKP3xj39U27ZtVbduXTk7O6tu3brq2bOn5s6dqwsXLtyOS7TJli1bZDKZ5ODgoO+++67cfteuXdPAgQNlMplUu3ZtJSYm3r4iy1HeZOeN2/79+8s8PjIyUpI0ffp0FRYW2lyH1eF34cKFmjBhgiZOnKh27dpp8eLF8vX11YoVK8rsv3LlSjVt2lSLFy9Wu3btNHHiRD399NN65513SvQzmUxq0KBBiQ0AABjP+fPnlZycLEny8vKSj4+PfHx8VLduXV2+fFmnTp3SwoUL1aVLF0u/682aNUuXL1/WjBkzVKtWrRL7PvzwQ0VGRmrnzp36z3/+o0uXLqlGjRq6cOGCvvjiC82ePVtt2rRRXFzcbblWaw0fPlx+fn4ym82aN29euf2mTJmiPXv2yMnJSZs2bVLnzp1vX5G34ODgYPkzLWtzdXUt87iAgAD1799fCQkJWr9+ve3nt6Zzfn6+4uPjFRwcXKI9ODhYX3zxRZnHxMXFlerfv39/HT9+XFevXrW05eTkqFmzZmrSpImGDBmihISEm9aSl5en7OzsEhsAALB/8fHxlq8PHjyotLQ0paWlKSMjQxcuXNDkyZMlSSkpKZo1a1aJY1NSUrRhwwa5uLjo6aefLjV29+7d9fbbbysuLk6//fabLl++rOzsbF28eFHR0dGqV6+eMjIyNGzYMGVlZf2+F2oDk8mkmTNnSpI++eQT/fDDD6X6zJs3T6tXr5ZUtFR1wIABt7XGW/H19bX8mZa1BQUFlXts8Z99ZZazWBV+MzIyVFBQIB8fnxLtPj4+SktLK/OYtLS0Mvtfu3ZNGRkZkqS2bdsqOjpaO3bsUExMjNzc3NSzZ0+dPn263FrmzZsnT09Py+br62vNpQAAgDtUcfh1dnZWu3btSuzz8vLSsmXL1L59e0nSrl27Sux///33VVBQoEGDBqlOnTqlxh43bpymT5+ugIAA3XPPPZZ2d3d3jR8/3jKjmJ6erk8//bQqL6uU7Oxsbd26Vd9//71Vx40ePVr33nuvCgoK9Oabb5bYFxMTY/mBYObMmXrmmWeqrN4bFRYW6uDBg/rpp59+t3PcqPjP9bvvvtM///lPm8aw6QNvJpOpxGuz2Vyq7Vb9r28PCAjQE088oU6dOikoKEh/+9vfdN9992np0qXljhkeHq6srCzLVtavPQAAgP05ceKEJMnPz08uLi6l9js4OKhbt26SipZIFBQUSCrKFx988IEkacyYMTadOyAgwPL1zz//bNMYN/P111/rzTffVO/evVW3bl099thjVodfR0dHvfLKK5Kkjz/+2FLn0aNH9dRTT8lsNmvMmDF6/fXXq7x+Sfq///s/hYeHq3nz5nrkkUd05syZ3+U8ZXFxcdFjjz0mSZbZbWs5WdPZ29tbjo6OpWZ509PTS83uFmvQoEGZ/Z2cnFS3bt0yjyn+S32zmV9XV9dy14QAAAD7VTzz26lTp3L75OfnSyqasXV0dJQkffvtt5YgeLNfnd/M9Xewuvfee20a43rZ2dnav3+/du3apT179iglJaXE/o4dO6px48ZWjzt+/HjNmTNHycnJeuedd/Tcc89p2LBhysvL08MPP6yPPvrophOT1kpPT1dMTIzWrVtXYlmKl5dXmTPsv6devXrp/fff1549e2w63qqZXxcXF/n7+2vfvn0l2vft26cePXqUeUxgYGCp/p999pm6du0qZ2fnMo8xm81KTExUw4YNrSkPAADYud9++80yk1he+DWbzZYPpD3wwAOW9iNHjkgqWlNqzQfn8/LydPbsWb333nsKCQmRJLVq1UpDhw616RrKmt394IMPlJKSInd3d/3xj3/UqlWrlJycrK+//lodO3a0+hzOzs6aMWOGpKKlHgMHDtSFCxfUrl07bdu2rcwZc2tdvnxZn3zyiQYPHqzGjRsrLCxM8fHxcnNz04gRI7Rt2zalpaXp/vvvt2rcc+fOyd/fX+7u7qpRo4ZatmypJ554QocOHarQ8Q8++KCkokD+73//29rLsm7mV5KmTZumkJAQde3aVYGBgVq9erWSkpIsC5DDw8OVkpKitWvXSipamPzee+9p2rRpeuaZZxQXF6cPPvhAMTExljGjoqIUEBCg1q1bKzs7W0uWLFFiYqKWLVtm9QUBAAD7VbzkQVK5dyhYtWqVJSCPHz/e0v7VV19JuvmM8fXc3NyUl5dXqr1nz57auHFjhX/DnJOTo71792r37t3avXu3fvnllxL777vvPg0aNEiDBg3Sww8/XCXBVJImTpyouXPnKi0tTWfOnJGPj4927dolLy8vm8c0m806fPiw1q1bp82bN1tuKODg4KBHHnlEY8eO1YgRI+Th4WHzOS5duqQTJ07Iy8tLubm5OnPmjM6cOaMNGzboqaee0urVq+XkVH5Ebd26tdzd3ZWTk6O4uDi1bdvWqvNbHX5HjRql8+fPa86cOUpNTVWHDh20a9cuNWvWTJKUmppa4p6/LVq00K5du/Tiiy9q2bJlatSokZYsWWJZryFJmZmZmjRpktLS0uTp6akuXbroyJEj6t69u7XlAQAAO3Z9+L0+xObn5+v06dP68MMPtXjxYknSI488UiL8FofOevXqVehcDRo00JUrV5STk6Pc3FxJUp8+ffTWW2+padOmFa558+bNeuqppyyv3dzc1Lt3bw0aNEiDBw9Wy5YtKzyWNZydndWqVSvL8tJ169apefPmNo116tQprVu3Ths2bCiR4zp37qwnnnhCjz/+uBo1alSpehs1aqSIiAgNHz5cbdq0kaurqwoKCvTVV18pIiJC+/fv10cffaRatWrd9HNfklS3bl3l5OSU+kGjIqwOv5IUGhqq0NDQMvdFR0eXanv44YdL/GW+0aJFi7Ro0SJbSgEAAHeR69eTent7l9tvzJgxWrVqlWW9ryTLQy8qugb17Nmzlq/T09O1bt06zZ07V927d9fs2bM1Z84cK6svUlBQoCtXrujKlSu6dOmSTWNUxPPPP69jx45ZXh89elT9+vWzepzY2FiNHj3a8rp58+YaM2aMxo4dKz8/vyqpVSq6Ne6Nt791dHRUjx49tHfvXg0fPlzbt2/X8uXL9cILL6h169bljlWnTh399NNP5T7o5GZsutsDAADA76F4sqxmzZqWhx40aNBArVq1UlBQkKZPn66EhARt2LBB7u7uJY69cuWKJNn0gfj69evrL3/5i/bs2SOTyaTXXnutwrc6Gzt2rD7//HO99NJLat++va5evapDhw5pxowZ6tixo3x9fTVp0iRt27atyp5LMG/ePK1cuVJS0eerJGnp0qU2jX/58mXL1zVq1NDIkSM1evToKg2+t+Lg4GB5AFphYaF27tx50/41atSQ9P//zK06l/XlAQAAVL3s7GzLbb8iIyMtDz1ITU3V6dOndeTIEb399tvlrgUuvovUb7/9ZnMN3bt310MPPSSp4rfScnZ2tiyX+Pbbb5WUlKSVK1fqj3/8o9zd3fXzzz/r/fff1/Dhw+Xt7W3p+80339hU44YNGyz38n311Ve1c+dOubu7KzMzU8uXL7d6vIEDByoqKkqtW7fW5cuX9dZbb+n+++9Xx44dNX/+/Nt2H99WrVpZZvt//PHHm/YtfgR1eXcOuxnCLwAAuCMkJCRYngXQtWtXq48vXutbHIxsVXzrMWvvv1vM19dXzz77rLZv367z589r3759mjZtmtq2bWuZFX755Zd1//33q0mTJiWWetzK559/rqefflpms1njx49XVFSU6tata7nxwKJFi0rM5FaEj4+PXn31Vf33v/9VXFycQkNDVbduXX377bcKDw9XixYtFBQUpJUrV+r8+fNWjf17Kf4zruj67usRfgEAwB2heMmDyWQqcQuziir+Nf2tZg1vpfj42rVrV2ocqeg2sX379tWCBQt06tQpnTlzRsuWLdPgwYNVs2ZNpaSkVHjd6rfffqvhw4crPz9f/fr10/vvv2/ZN336dLm5uSk9Pb1Eu7UCAgK0bNkypaamatu2bRo+fLhcXFx07NgxPffcc2rYsKGGDh2qTz75pMrXM//www+Wp/+2aNGi3H4XL1609LvxCYAVQfgFAAB3hOIZ0HvvvVeenp5WH9+rVy9J0smTJ8u8hVlBQYFlZrk8Bw4c0P/+7/9Kknr37m11DbfSvHlzhYaG6tNPP9WFCxe0Z88etWnT5pbHpaSkaODAgcrKylKnTp20efPmEs9L8PHx0cSJEyVJb7/9tuUhILZydnbWsGHDtGXLFqWmpmrlypXq2bOnrl69qk8//VSPP/64fHx8FBISUqE7LtzqfTebzXrppZckFa3/HTJkSLl9jx8/rsLCQjk5Oalnz57WXZgIvwAA4A5RPPNry5IHqej+vE5OTsrPz1diYmKp/cnJyerSpYtWrVqlH3/8sUQgS05O1vz58/Xoo4/KbDarTp06evHFFyt03ry8PGVkZFi9Xbx4Uf7+/mrSpMlNx8/OztagQYP0888/y9fXV//4xz/KvM/uyy+/LBcXF/3888+W5y1UBS8vLz377LM6duyYfvjhB0VGRqpVq1bKycnR+vXr9d///veWY/z000/q3r17qfe+sLBQX375pQYOHKht27ZJkp599tmb/kBQfD/nBx54oNSHHivCpludAQAAVKXc3Fz95z//kST5+/vbNIaHh4cGDx6s7du3a8eOHZYngV3v5MmTlvWxLi4u8vDw0OXLly33+ZWKfuW+ZcuWCj8lLiYmpsR9fq21e/duDRgwoMx9V69e1fDhw/X111/L09NTu3btKvdxyE2aNNG4ceO0Zs0azZ8/X0899VSJW8FVhZYtWyoiIkIRERGKi4vTunXrKhxA//Wvf+lf//qXpKI7ctSuXVsXL14sMUv/1FNPacmSJTcdZ8eOHZKKbndnC2Z+AQBAtfvmm29UWFgoyfbwKxXNGkrSxo0bS/2qvVGjRvrb3/6m0NBQ+fv7y9vbW9nZ2SosLFTTpk01dOhQrVmzRt999526dOli+8VUoQkTJujAgQNydnbW1q1b1aFDh5v2Dw8Pl5OTk3744QfFxsb+rrUFBgZq+fLlFZqp9/Hx0dKlSzVmzBj5+fnJw8NDmZmZcnZ2Vtu2bfX000/r2LFj+vDDD2/6dLczZ84oLi5ONWrU0Lhx42yq22S+1SIMO5GdnS1PT09lZWVV6pF71S0qKqq6S7gjREREVHqMszJVQSX2r7kq/y3Oe1mksu8l399FquL7G3ePqv7/u7CwUPfdd59++OEHHT582LIOGHeHOXPmKCIiQk899ZQ+/PBDm8Zg5hcAANw1HBwc9Nprr0mS5s+fX83VoCrl5uZq6dKlcnV1rdQP0YRfAABwVxk9erS6d++u3bt3Wz4cBfv33nvvKSMjQy+88IKaNWtm8zh84A0AANxVTCaTVq1apb///e+W+8HC/tWqVUuRkZEKCwur1DiEXwAAcNfp3LlzuY9Bhn16/vnnq2Qclj0AAADAMAi/AAAAMAzCLwAAAAyD8AsAAADDIPwCAADAMAi/AADArly8eFGRkZHq2LGj3N3d5enpqW7dumnBggXKz8+3edzIyEiZTKZbbt9//30VXg1uN251BgAA7MZPP/2k3r176+zZs5KkmjVrKi8vT8ePH9fx48e1YcMGHThwQF5eXjafw9nZWXXq1Cl3v5MT8cmeMfMLAADsQkFBgYYOHaqzZ8+qYcOG2rdvn3Jzc3Xp0iV98sknql27thISEjR27NhKnadHjx5KS0srd2vevHnVXBCqBeEXAADYhejoaH3zzTeSpC1btqhv376SJAcHB40aNUqrVq2SJO3evVsHDhyotjpxZyP8AgAAu/Dxxx9Lkvr06aPAwMBS+0ePHq0WLVpIktauXXtba4P9IPwCAIA73qVLl/TPf/5TkjRw4MAy+5hMJg0YMECS9Nlnn9222mBfCL8AAOCOd+rUKRUWFkqSOnToUG6/4n1paWm6cOGCTef67rvv1KFDB9WoUUPu7u5q06aNnnnmGSUkJNg0Hu4shF8AAHDH++WXXyxfN27cuNx+1++7/hhrZGRk6NSpU5Y7Sfz3v//VmjVr5O/vr9mzZ9s0Ju4chF8AAHDHu3jxouXrmjVrltvv+n3XH1MRrVu31ltvvaX//Oc/unLlis6fP6/c3Fzt3btX/v7+MpvNmjt3rhYsWGD9BeCOQfgFAACQNHbsWL300ku677775OzsLElycXFRcHCwjh07pm7dukkqehhGVlZWdZaKSiD8AgCAO17t2rUtX1+6dKncftfvu/6YynJzc9Mbb7whScrJyeFWanaM8AsAAO54jRo1snydkpJSbr/r911/TFW4/vZqP/74Y5WOjduH8AsAAO547dq1k4NDUWz59ttvy+1XvK9BgwY3fUQxjIvwCwAA7ng1a9ZUz549JUl79uwps4/ZbNbevXslScHBwVVew5dffmn5uvhhGrA/hF8AAGAXxo8fL0k6ePCgvvrqq1L7N23aZFmOMG7cOKvGNpvNN92fl5enWbNmSZJq1aqlP/zhD1aNjzsH4RcAANiF8ePHq2PHjjKbzXrssccsHzorLCzUpk2b9Mwzz0gqegJcWeE0MjJSJpNJJpNJZ8+eLbHvyJEj6tu3r9avX6+ff/7Z0n716lUdOHBAQUFBlsD96quv6p577vl9LhK/O6fqLgAAAKAinJyctGPHDvXp00dnz55V3759VbNmTRUWFurKlSuSpC5dumjDhg1Wj202m3XgwAFLoK5Ro4Zq1aqlrKwsXb16VZLk4OCgV155RTNmzKi6i8JtR/gFAAB2o3nz5vr666/1zjvvaOvWrTpz5oycnZ3Vvn17Pf744/rzn/8sFxcXq8ft2LGj3nnnHcXFxembb75RRkaGMjMzVbNmTfn5+SkoKEiTJk1Sx44df4erwu1E+AUAAHaldu3aioqKUlRUlFXHRUZGKjIyssx9devW1V/+8pcqqA53Otb8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMg/ALAAAAwyD8AgAAwDAIvwAAADAMwi8AAAAMw6bwu3z5crVo0UJubm7y9/fX0aNHb9r/8OHD8vf3l5ubm1q2bKmVK1eW6rNlyxb5+fnJ1dVVfn5+2rZtmy2lAQAAAOWyOvzGxsYqLCxMs2bNUkJCgoKCgjRw4EAlJSWV2f/MmTMaNGiQgoKClJCQoJkzZ+qFF17Qli1bLH3i4uI0atQohYSE6OTJkwoJCdHIkSP11Vdf2X5lAAAAwA1MZrPZbM0BDz74oB544AGtWLHC0tauXTsNGzZM8+bNK9X/5Zdf1o4dO3Tq1ClL2+TJk3Xy5EnFxcVJkkaNGqXs7Gzt3r3b0mfAgAHy8vJSTExMmXXk5eUpLy/P8jorK0tNmzZVcnKyPDw8rLmkO0pZ76ERhYeHV3qMn+RZBZXYv2bKqvQYvJdFKvte8v1dpCq+v3H3yM7Olq+vrzIzM+Xpyb81uA3MVsjLyzM7Ojqat27dWqL9hRdeMPfq1avMY4KCgswvvPBCibatW7eanZyczPn5+Waz2Wz29fU1L1y4sESfhQsXmps2bVpuLREREWZJbGxsbGxsbHfBlpycbE0kAWzmJCtkZGSooKBAPj4+Jdp9fHyUlpZW5jFpaWll9r927ZoyMjLUsGHDcvuUN6ZUNHMwbdo0y+vMzEw1a9ZMSUlJ/ORYCcU/gdv7DPqdgPey6vBeVg3ex6rDe1l1zGazLl68qEaNGlV3KTAIq8JvMZPJVOK12Wwu1Xar/je2Wzumq6urXF1dS7V7enryD1EV8PDw4H2sIryXVYf3smrwPlYd3suqwaQVbierPvDm7e0tR0fHUjOy6enppWZuizVo0KDM/k5OTqpbt+5N+5Q3JgAAAGALq8Kvi4uL/P39tW/fvhLt+/btU48ePco8JjAwsFT/zz77TF27dpWzs/NN+5Q3JgAAAGALq5c9TJs2TSEhIeratasCAwO1evVqJSUlafLkyZKK1uKmpKRo7dq1koru7PDee+9p2rRpeuaZZxQXF6cPPvigxF0cpk6dql69eunNN9/Uo48+qu3bt2v//v06duxYhetydXVVREREmUshUHG8j1WH97Lq8F5WDd7HqsN7Cdgvq291JhU95OKtt95SamqqOnTooEWLFqlXr16SpCeffFJnz57VoUOHLP0PHz6sF198Ud99950aNWqkl19+2RKWi23evFmzZ8/Wjz/+qHvvvVdz587V8OHDK3d1AAAAwHVsCr8AAACAPbLp8cYAAACAPSL8AgAAwDAIvwAAADAMuw6/Fy9e1IwZMxQcHKx69erJZDIpMjKyusuyO59//rmefvpptW3bVrVq1VLjxo316KOPKj4+vrpLszuJiYkaPHiwmjZtqho1aqhOnToKDAzU+vXrq7s0u7dmzRqZTCa5u7tXdyl25dChQzKZTGVuX375ZXWXZ5eOHTumQYMGycvLSzVq1FDr1q312muvVXdZACrIpie83SnOnz+v1atXq1OnTho2bJjWrFlT3SXZpRUrVuj8+fOaOnWq/Pz8dO7cOS1YsEABAQHau3evHnnkkeou0W5kZmbK19dXjz/+uBo3bqzc3Fxt2LBBISEhOnv2rGbPnl3dJdqllJQUTZ8+XY0aNVJWVlZ1l2OX3njjDfXp06dEW4cOHaqpGvu1ceNGhYSEaOTIkVq7dq3c3d31ww8/6Jdffqnu0gBUkF3f7eH6xyRnZGSoXr16ioiIYPbXSunp6apfv36JtpycHLVq1UodOnTQ/v37q6myu0dAQIB++eUXJSUlVXcpdmno0KEymUyqU6eONm/erJycnOouyW4cOnRIffr00aZNmzRixIjqLseupaSkqE2bNho3bpyWL19e3eUAsJFdL3so/tUdKufG4CtJ7u7u8vPzU3JycjVUdPfx9vaWk5Nd/6Kl2qxfv16HDx8mbKDarVmzRrm5uXr55ZeruxQAlWDX4Re/n6ysLJ04cULt27ev7lLsUmFhoa5du6Zz585p+fLl2rt3L/9h2iA9PV1hYWGaP3++mjRpUt3l2LUpU6bIyclJHh4e6t+/v1VP0ESRI0eOqE6dOvr3v/+tzp07y8nJSfXr19fkyZOVnZ1d3eUBqCDCL8o0ZcoU5ebmatasWdVdil0KDQ2Vs7Oz6tevrxdffFFLlizRs88+W91l2Z3Q0FC1adNGzz33XHWXYrc8PT01depUrVq1SgcPHtS7776r5ORk9e7dW3v37q3u8uxKSkqKLl26pP/5n//RqFGjtH//fr300ktau3atBg0aJDteRQgYCr+HRSl//etftWHDBi1dulT+/v7VXY5dmjlzpiZOnKj09HTt3LlTzz//vHJzczV9+vTqLs1ubNmyRTt37lRCQgLLmyqhS5cu6tKli+V1UFCQ/vSnP6ljx46aMWOG+vfvX43V2ZfCwkJduXJFEREReuWVVyRJvXv3louLi8LCwnTgwAH17du3mqsEcCvM/KKEqKgovf7665o7d66ef/756i7HbjVt2lRdu3bVoEGDtGLFCk2aNEnh4eE6d+5cdZdmF3JycjRlyhT9+c9/VqNGjZSZmanMzEzl5+dLKrqrRm5ubjVXab/uueceDRkyRF9//bUuX75c3eXYjbp160pSqR8YBg4cKEk6ceLEba8JgPUIv7CIiopSZGSkIiMjNXPmzOou567SvXt3Xbt2TT/++GN1l2IXMjIy9Ouvv2rBggXy8vKybDExMcrNzZWXl5fGjh1b3WXatevvloOKuf/++8tsL34vHRz4LxWwByx7gCTptddeU2RkpGbPnq2IiIjqLueuc/DgQTk4OKhly5bVXYpdaNCggQ4ePFiqff78+Tp8+LB2794tb2/vaqjs7vDbb7/p008/VefOneXm5lbd5diNxx57TKtXr9bu3btLLCXZtWuXpKJbGgK489l9+N29e7dyc3N18eJFSdL//d//afPmzZKkQYMGqWbNmtVZnl1YsGCBXn31VQ0YMECDBw8u9dQn/kGvuEmTJsnDw0Pdu3eXj4+PMjIytGnTJsXGxuqll15SvXr1qrtEu+Dm5qbevXuXao+Ojpajo2OZ+1C2MWPGWJbheHt76/Tp01qwYIF+/fVXRUdHV3d5diU4OFhDhw7VnDlzVFhYqICAAB0/flxRUVEaMmSIHnrooeouEUAF2PVDLiSpefPm+umnn8rcd+bMGTVv3vz2FmSHevfurcOHD5e7387/itxWH330kT766COdOnVKmZmZcnd3V6dOnTRx4kQ98cQT1V2e3XvyySd5yIWV5s+fr9jYWJ05c0Y5OTmqU6eOHnroIYWHh6tbt27VXZ7duXz5sqKiorRx40alpqaqUaNGGjt2rCIiIuTq6lrd5QGoALsPvwAAAEBFsTofAAAAhkH4BQAAgGEQfgEAAGAYhF8AAAAYBuEXAAAAhkH4BQAAgGEQfgEAAGAYhF8AAAAYBuEXAAAAhkH4BQAAgGEQfgEAAGAY/w8pFEYi5DC9lwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X))\n",
    "x2 = list(np.arange(X,Y))\n",
    "x3 = list(np.arange(Y,Y+10))\n",
    "plt.bar(x1, randint.pmf(x1, a, b+1), color ='gray')\n",
    "plt.bar(x2, randint.pmf(x2, a, b+1), color ='#DFFF00')\n",
    "plt.bar(x3, randint.pmf(x3, a, b+1), color ='gray')\n",
    "plt.xlim(a-1,b+2)\n",
    "plt.xticks(np.arange(a-1,b+2), fontsize=12, ha='center')\n",
    "plt.title(f'$U\\ {r}$')\n",
    "xs = np.arange(X, Y)\n",
    "prob = np.sum([randint.pmf(xs, a, b+1) for xs in xs])\n",
    "plt.text(7, 0.02, f'$P({np.round(X, 3)} \\leq X < {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8n2NKgASvThs"
   },
   "source": [
    "To find the probability between two points $(X,Y]$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "1V6w3MxivThs",
    "outputId": "3c146a5d-9386-4862-dd19-be26a51371a2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *(3, 5]* in the U[2, 3, 4, 5] Distribution is:  0.5\n"
     ]
    }
   ],
   "source": [
    "X = 3\n",
    "Y = 5\n",
    "a, b = [2,5]\n",
    "r = list(np.arange(a, b+1))\n",
    "xs = np.arange(X+1, Y+1)\n",
    "print(f'The probability between *({X}, {Y}]* in the U{r} Distribution is: ', np.sum([randint.pmf(xs, a, b+1) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "id": "2gI6cwM-vTht",
    "outputId": "505d6e04-21a7-4347-ffa0-99cbf99bf460"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X+1))\n",
    "x2 = list(np.arange(X+1,Y+1))\n",
    "x3 = list(np.arange(Y+1,Y+10))\n",
    "plt.bar(x1, randint.pmf(x1, a, b+1), color ='gray')\n",
    "plt.bar(x2, randint.pmf(x2, a, b+1), color ='#DFFF00')\n",
    "plt.bar(x3, randint.pmf(x3, a, b+1), color ='gray')\n",
    "plt.xlim(a-1,b+2)\n",
    "plt.xticks(np.arange(a-1,b+2), fontsize=12, ha='center')\n",
    "plt.title(f'$U\\ {r}$')\n",
    "xs = np.arange(X+1, Y+1)\n",
    "prob = np.sum([randint.pmf(xs, a, b+1) for xs in xs])\n",
    "plt.text(7, 0.02, f'$P({np.round(X, 3)} < X \\leq {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "WcMTHtMnvzer"
   },
   "source": [
    "To find the probability of a point use the code below:\n",
    "\n",
    "''\n",
    "randint.pmf($X, a, b+1$)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "dXbmT6Dqvzes",
    "outputId": "8afc8446-9e98-451d-b0c1-767ce6781db2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of *X=3* in the U[2, 3, 4, 5] Distribution is:  0.25\n"
     ]
    }
   ],
   "source": [
    "X = 3\n",
    "a, b = [2,5]\n",
    "print(f'The probability of *X={X}* in the U{r} Distribution is: ', randint.pmf(X, a, b+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "id": "_nYvQeMdvzet",
    "outputId": "044590fc-2c04-4ba3-f420-0db3fa60b83c"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X))\n",
    "x2 = X\n",
    "x3 = list(np.arange(X+1,Y+10))\n",
    "plt.bar(x1, randint.pmf(x1, a, b+1), color ='gray')\n",
    "plt.bar(x2, randint.pmf(x2, a, b+1), color ='#DFFF00')\n",
    "plt.bar(x3, randint.pmf(x3, a, b+1), color ='gray')\n",
    "plt.xlim(a-1,b+2)\n",
    "plt.xticks(np.arange(a-1,b+2), fontsize=12, ha='center')\n",
    "plt.title(f'$U\\ {r}$')\n",
    "prob = randint.pmf(x2, a, b+1)\n",
    "plt.text(7, 0.02, f'$P({np.round(X, 3)}) = $ {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tDQwSzWJeoz2"
   },
   "source": [
    "<a name='Hypergeometric_Distribution'></a>\n",
    "\n",
    "## **2.7. Hypergeometric Distribution:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "j_Ddl6KBeuif"
   },
   "source": [
    "$P(X=i) = \\frac{\\binom{i}{m} \\binom{N-m}{n-i}}{\\binom{N}{n}} \\quad \\quad N = 0,1,2,...,\\infty$\n",
    "\n",
    "$\\ \\qquad \\qquad \\qquad \\qquad \\qquad \\quad m = 0,1,2,...,N$\n",
    "\n",
    "$\\ \\qquad \\qquad \\qquad \\qquad \\qquad \\quad n = 0,1,2,...,N$\n",
    "\n",
    "$\\\\ $\n",
    "\n",
    "$E(X) = \\frac{mn}{N}$\n",
    "\n",
    "$Var(X) = n \\frac{m}{N} (1-\\frac{m}{N}) \\frac{N-n}{N-1}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 281
    },
    "id": "zvp0BN9NgXxe",
    "outputId": "536d2b8b-85e4-426a-80a8-419612cc5cc3"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "s = 1000000\n",
    "m, N, n = [50, 500, 100]\n",
    "\n",
    "hg_data = np.random.hypergeometric(ngood = m, nbad = N-m, nsample = n, size=s)\n",
    "\n",
    "sns.histplot(hg_data, color='cyan', stat='density', bins=50)\n",
    "\n",
    "plt.title('Hypergeometric Distribution');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "XapaJszTiRbx",
    "outputId": "3f521894-3054-4e72-c4d5-af796a18e60b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the HG(500, 50, 100) Distribution is:  10.0\n",
      "The median of the HG(500, 50, 100) Distribution is:  10.0\n",
      "The variance of the HG(500, 50, 100) Distribution is:  7.2144\n",
      "The standard deviation of the HG(500, 50, 100) Distribution is:  2.686\n",
      "The skewness of the HG(500, 50, 100) Distribution is:  0.1794\n",
      "The kurtosis of the HG(500, 50, 100) Distribution is:  -0.0093\n"
     ]
    }
   ],
   "source": [
    "m, N, n = [50, 500, 100]\n",
    "print(f'The mean of the HG{N,m,n} Distribution is: ', np.round(hypergeom.mean(n = m, M = N, N = n), 4))\n",
    "print(f'The median of the HG{N,m,n} Distribution is: ', np.round(hypergeom.median(n = m, M = N, N = n), 4))\n",
    "print(f'The variance of the HG{N,m,n} Distribution is: ', np.round(hypergeom.var(n = m, M = N, N = n), 4))\n",
    "print(f'The standard deviation of the HG{N,m,n} Distribution is: ', np.round(hypergeom.std(n = m, M = N, N = n), 4))\n",
    "print(f'The skewness of the HG{N,m,n} Distribution is: ', np.round(hypergeom.stats(n = m, M = N, N = n, moments='mvsk')[2], 4))\n",
    "print(f'The kurtosis of the HG{N,m,n} Distribution is: ', np.round(hypergeom.stats(n = m, M = N, N = n, moments='mvsk')[3], 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7hoHUIgXkKhe"
   },
   "source": [
    "Integrating the PDF, gives us the cumulative distribution function (CDF) which is a function that maps values to their percentile rank in a distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "id": "FXwHrJonkKhg",
    "outputId": "6511b1b2-127c-4b5e-af9d-a1c86961ee9a"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m, N, n = [50, 500, 100]\n",
    "x = np.arange(0, m+1, 0.001)\n",
    "x1 = np.arange(0, m+1)\n",
    "x2 = np.arange(0, m) + 0.999\n",
    "\n",
    "plt.scatter(x, hypergeom.cdf(x, n = m, M = N, N = n), color = 'r')\n",
    "plt.scatter(x2, hypergeom.cdf(x2, n = m, M = N, N = n), color = 'white', edgecolor='black', s=80)\n",
    "plt.scatter(x1, hypergeom.cdf(x1, n = m, M = N, N = n), color = 'black', edgecolor='black', s=80)\n",
    "plt.xlim(1,16.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6RmpKhJXmP1p"
   },
   "source": [
    "To find the left probability of a point use the code below:\n",
    "\n",
    "''\n",
    "hypergeom.cdf(X, n = m, M = N, N = n)\n",
    "''\n",
    "\n",
    "To find the right probability of a point use the code below:\n",
    "\n",
    "''\n",
    "hypergeom.sf(X, n = m, M = N, N = n)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "DWf8ovrcmP1q",
    "outputId": "190cb736-7980-4cda-ef12-bd70618e662c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The left probability of *9* in the HG(500, 50, 100) Distribution is:  0.4377805207673867\n",
      "The Right probability of *9* in the HG(500, 50, 100) Distribution is:  0.5622194792326133\n"
     ]
    }
   ],
   "source": [
    "X = 9\n",
    "m, N, n = [50, 500, 100]\n",
    "print(f'The left probability of *{X}* in the HG{N,m,n} Distribution is: ', hypergeom.cdf(X, n = m, M = N, N = n))\n",
    "print(f'The Right probability of *{X}* in the HG{N,m,n} Distribution is: ', hypergeom.sf(X, n = m, M = N, N = n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FygbTGmJmvRn"
   },
   "source": [
    "To find the probability between two points $[X,Y]$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "SrXujRTcmvRq",
    "outputId": "16093086-deb2-4d21-d548-cbd025aaa169"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *[5, 8]* in the HG(500, 50, 100) Distribution is:  0.2812099969935373\n"
     ]
    }
   ],
   "source": [
    "X = 5\n",
    "Y = 8\n",
    "m, N, n = [50, 500, 100]\n",
    "xs = np.arange(X, Y+1)\n",
    "print(f'The probability between *[{X}, {Y}]* in the HG{N,m,n} Distribution is: ', np.sum([hypergeom.pmf(xs, n = m, M = N, N = n) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "id": "VRV5t4temvRs",
    "outputId": "a785d225-09bc-458c-c290-6dcd5d5f5404"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X))\n",
    "x2 = list(np.arange(X,Y+1))\n",
    "x3 = list(np.arange(Y+1,22))\n",
    "plt.bar(x1, hypergeom.pmf(x1, n = m, M = N, N = n), color ='gray')\n",
    "plt.bar(x2, hypergeom.pmf(x2, n = m, M = N, N = n), color ='#DFFF00')\n",
    "plt.bar(x3, hypergeom.pmf(x3, n = m, M = N, N = n), color ='gray')\n",
    "plt.xlim(0, 22)\n",
    "plt.xticks(np.arange(0,22), fontsize=12, ha='center')\n",
    "plt.title(f'$HG{N,m,n}$')\n",
    "xs = np.arange(X, Y+1)\n",
    "prob = np.sum([hypergeom.pmf(xs, n = m, M = N, N = n) for xs in xs])\n",
    "plt.text(15, 0.02, f'$P({np.round(X, 3)} \\leq X \\leq {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TKmPFkT-nmm3"
   },
   "source": [
    "To find the probability between two points $(X,Y)$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "eKlarBDmnmm6",
    "outputId": "a247dca5-b8b0-46ae-da0d-40165a5cbede"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *(5, 8)* in the HG(500, 50, 100) Distribution is:  0.13660350069991276\n"
     ]
    }
   ],
   "source": [
    "X = 5\n",
    "Y = 8\n",
    "m, N, n = [50, 500, 100]\n",
    "xs = np.arange(X+1, Y)\n",
    "print(f'The probability between *({X}, {Y})* in the HG{N,m,n} Distribution is: ', np.sum([hypergeom.pmf(xs, n = m, M = N, N = n) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "id": "7NIq8laNnmm8",
    "outputId": "9ac4e4b0-a12e-4b93-dd63-145abd0e34a6"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JCVq2bKm1mkRERNRw6anTOTs7G2VlZbC0tFRot7S0RGZmptYGNXv2bFhbW6N///5V9ikqKkJRUZH867y8PK1tn4iIiMRFo5NuJRKJwteCICi1aWrRokXYvHkzfvrpJ0il0ir7RUREwMTERL7Y2NhoZftEREQkPmoFFnNzc+jq6irNpmRlZSnNumhiyZIlWLhwIfbv34/OnTtX2zc4OBi5ubny5datW7XePhEREYmTWoeEDAwMIJPJkJCQgCFDhsjbExISMGjQoFoNZPHixfjss8+wb98+uLq6PrO/oaEhDA0Na7VNouclLCxMK3VCQ0O1UoeISOzUCiwAEBQUhLFjx8LV1RVubm5YtWoV0tLS4O/vD6Bi5iM9PR3r1q2Tr3Pu3DkAQEFBAe7evYtz587BwMAAzs7OACoOA82bNw+bNm2Cvb29fAbH2NgYxsbGtX2PRERE1MCpHVhGjhyJnJwchIeHIyMjAy4uLoiPj4ednR2AihvFPX1Plm7dusn/nZSUhE2bNsHOzg6pqakAKm5EV1xcjOHDhyusFxoaivnz56s7RCIiImpk1A4sABAQEICAgACVr8XGxiq1CYJQbb3K4EJERESkCp8lRERERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKKn97wHQERUV8LCwrRSJzQ0VCt1iEhznGEhIiIi0WNgISIiItFjYCEiIiLRY2AhIiIi0WNgISIiItFjYCEiIiLRY2AhIiIi0WNgISIiItFjYCEiIiLRY2AhIiIi0WNgISIiItHTKLAsX74cbdu2hVQqhUwmw9GjR6vsm5GRAV9fX3Ts2BE6OjoIDAxU2W/79u1wdnaGoaEhnJ2dsWPHDk2GRkRERI2Q2oElLi4OgYGBCAkJQXJyMtzd3eHt7Y20tDSV/YuKimBhYYGQkBB06dJFZZ/ExESMHDkSY8eOxfnz5zF27FiMGDECp06dUnd4RERE1AipHViWLl2KSZMmwc/PD05OToiMjISNjQ1WrFihsr+9vT2++eYbjBs3DiYmJir7REZGwsPDA8HBwXB0dERwcDBef/11REZGqjs8IiIiaoTUCizFxcVISkqCp6enQrunpydOnDih8SASExOVanp5eVVbs6ioCHl5eQoLERERNU5qBZbs7GyUlZXB0tJSod3S0hKZmZkaDyIzM1PtmhERETAxMZEvNjY2Gm+fiIiIxE2jk24lEonC14IgKLXVdc3g4GDk5ubKl1u3btVq+0RERCReeup0Njc3h66urtLMR1ZWltIMiTpatWqldk1DQ0MYGhpqvE0iIiJqONSaYTEwMIBMJkNCQoJCe0JCAnr27KnxINzc3JRq7t+/v1Y1iYiIqPFQa4YFAIKCgjB27Fi4urrCzc0Nq1atQlpaGvz9/QFUHKpJT0/HunXr5OucO3cOAFBQUIC7d+/i3LlzMDAwgLOzMwBg+vTp6N27N7788ksMGjQIv/zyCw4cOIBjx45p4S0SERFRQ6d2YBk5ciRycnIQHh6OjIwMuLi4ID4+HnZ2dgAqbhT39D1ZunXrJv93UlISNm3aBDs7O6SmpgIAevbsiS1btmDu3LmYN28eHBwcEBcXh1dffbUWb42IiIgaC7UDCwAEBAQgICBA5WuxsbFKbYIgPLPm8OHDMXz4cE2GQ0RERI0cnyVEREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKKn97wHQCRmqZBopY49BK3UISL6r+IMCxEREYkeAwsRERGJHgMLERERiR4DCxEREYkeAwsRERGJHgMLERERiR4DCxEREYmeRoFl+fLlaNu2LaRSKWQyGY4ePVpt/yNHjkAmk0EqlaJdu3aIiopS6hMZGYmOHTvCyMgINjY2mDFjBh4/fqzJ8IiIiKiRUTuwxMXFITAwECEhIUhOToa7uzu8vb2Rlpamsn9KSgp8fHzg7u6O5ORkzJkzB9OmTcP27dvlfTZu3IjZs2cjNDQUly9fRkxMDOLi4hAcHKz5OyMiIqJGQ+073S5duhSTJk2Cn58fgIqZkX379mHFihWIiIhQ6h8VFQVbW1tERkYCAJycnHDmzBksWbIEw4YNAwAkJiaiV69e8PX1BQDY29tj9OjROH36tKbvi4iIiBoRtWZYiouLkZSUBE9PT4V2T09PnDhxQuU6iYmJSv29vLxw5swZlJSUAABee+01JCUlyQPKjRs3EB8fjzfffLPKsRQVFSEvL09hISIiosZJrRmW7OxslJWVwdLSUqHd0tISmZmZKtfJzMxU2b+0tBTZ2dlo3bo1Ro0ahbt37+K1116DIAgoLS3F5MmTMXv27CrHEhERgbCwMHWGT0RERA2URifdSiSKD4QTBEGp7Vn9n2w/fPgwPv/8cyxfvhxnz57FTz/9hF27dmHBggVV1gwODkZubq58uXXrliZvhYiIiBoAtWZYzM3NoaurqzSbkpWVpTSLUqlVq1Yq++vp6cHMzAwAMG/ePIwdO1Z+XkynTp1QWFiI999/HyEhIdDRUc5VhoaGMDQ0VGf4RERE1ECpNcNiYGAAmUyGhIQEhfaEhAT07NlT5Tpubm5K/ffv3w9XV1fo6+sDAB4+fKgUSnR1dSEIgnw2hoiIiP671D4kFBQUhNWrV2PNmjW4fPkyZsyYgbS0NPj7+wOoOFQzbtw4eX9/f3/cvHkTQUFBuHz5MtasWYOYmBjMnDlT3mfgwIFYsWIFtmzZgpSUFCQkJGDevHl46623oKurq4W3SURERA2Z2pc1jxw5Ejk5OQgPD0dGRgZcXFwQHx8POzs7AEBGRobCPVnatm2L+Ph4zJgxA99//z2srKywbNky+SXNADB37lxIJBLMnTsX6enpsLCwwMCBA/H5559r4S0SERFRQ6d2YAGAgIAABAQEqHwtNjZWqa1Pnz44e/Zs1YPQ00NoaChCQ0M1GQ4RERE1cnyWEBEREYkeAwsRERGJHgMLERERiR4DCxEREYmeRifdEhH912nr0SC82ICoZjjDQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESip1FgWb58Odq2bQupVAqZTIajR49W2//IkSOQyWSQSqVo164doqKilPo8ePAAU6ZMQevWrSGVSuHk5IT4+HhNhkdERESNjNqBJS4uDoGBgQgJCUFycjLc3d3h7e2NtLQ0lf1TUlLg4+MDd3d3JCcnY86cOZg2bRq2b98u71NcXAwPDw+kpqZi27ZtuHLlCqKjo2Ftba35OyMiIqJGQ0/dFZYuXYpJkybBz88PABAZGYl9+/ZhxYoViIiIUOofFRUFW1tbREZGAgCcnJxw5swZLFmyBMOGDQMArFmzBvfu3cOJEyegr68PALCzs9P0PREREVEjo9YMS3FxMZKSkuDp6anQ7unpiRMnTqhcJzExUam/l5cXzpw5g5KSEgDAr7/+Cjc3N0yZMgWWlpZwcXHBwoULUVZWVuVYioqKkJeXp7AQERFR46RWYMnOzkZZWRksLS0V2i0tLZGZmalynczMTJX9S0tLkZ2dDQC4ceMGtm3bhrKyMsTHx2Pu3Ln46quv8Pnnn1c5loiICJiYmMgXGxsbdd4KERERNSAanXQrkUgUvhYEQantWf2fbC8vL8cLL7yAVatWQSaTYdSoUQgJCcGKFSuqrBkcHIzc3Fz5cuvWLU3eChERETUAap3DYm5uDl1dXaXZlKysLKVZlEqtWrVS2V9PTw9mZmYAgNatW0NfXx+6urryPk5OTsjMzERxcTEMDAyU6hoaGsLQ0FCd4RMREVEDpdYMi4GBAWQyGRISEhTaExIS0LNnT5XruLm5KfXfv38/XF1d5SfY9urVC9euXUN5ebm8z9WrV9G6dWuVYYWIiIj+W9Q+JBQUFITVq1djzZo1uHz5MmbMmIG0tDT4+/sDqDhUM27cOHl/f39/3Lx5E0FBQbh8+TLWrFmDmJgYzJw5U95n8uTJyMnJwfTp03H16lXs3r0bCxcuxJQpU7TwFomIiKihU/uy5pEjRyInJwfh4eHIyMiAi4sL4uPj5ZchZ2RkKNyTpW3btoiPj8eMGTPw/fffw8rKCsuWLZNf0gwANjY22L9/P2bMmIHOnTvD2toa06dPxyeffKKFt0hEREQNndqBBQACAgIQEBCg8rXY2Filtj59+uDs2bPV1nRzc8PJkyc1GQ4RERE1cnyWEBEREYkeAwsRERGJHgMLERERiR4DCxEREYkeAwsRERGJHgMLERERiR4DCxEREYkeAwsRERGJHgMLERERiR4DCxEREYkeAwsRERGJHgMLERERiR4DCxEREYmeRk9rJhKTVEi0UsceglbqEBGR9nGGhYiIiESPgYWIiIhEj4GFiIiIRI+BhYiIiESPgYWIiIhEj4GFiIiIRI+BhYiIiESPgYWIiIhEjzeOIyISkbCwMK3UCQ0N1UodIrHgDAsRERGJHgMLERERiR4DCxEREYkeAwsRERGJHgMLERERiR4DCxEREYkeAwsRERGJHgMLERERiR4DCxEREYkeAwsRERGJHgMLERERiR4DCxEREYkeAwsRERGJnkaBZfny5Wjbti2kUilkMhmOHj1abf8jR45AJpNBKpWiXbt2iIqKqrLvli1bIJFIMHjwYE2GRkRERI2Q2oElLi4OgYGBCAkJQXJyMtzd3eHt7Y20tDSV/VNSUuDj4wN3d3ckJydjzpw5mDZtGrZv367U9+bNm5g5cybc3d3VfydERETUaKkdWJYuXYpJkybBz88PTk5OiIyMhI2NDVasWKGyf1RUFGxtbREZGQknJyf4+flh4sSJWLJkiUK/srIyjBkzBmFhYWjXrp1m74aIiIgaJbUCS3FxMZKSkuDp6anQ7unpiRMnTqhcJzExUam/l5cXzpw5g5KSEnlbeHg4LCwsMGnSJHWGRERERP8Beup0zs7ORllZGSwtLRXaLS0tkZmZqXKdzMxMlf1LS0uRnZ2N1q1b4/jx44iJicG5c+dqPJaioiIUFRXJv87Ly6v5GyEiIqIGRaOTbiUSicLXgiAotT2rf2V7fn4+3nnnHURHR8Pc3LzGY4iIiICJiYl8sbGxUeMdEBERUUOiVmAxNzeHrq6u0mxKVlaW0ixKpVatWqnsr6enBzMzM1y/fh2pqakYOHAg9PT0oKenh3Xr1uHXX3+Fnp4erl+/rrJucHAwcnNz5cutW7fUeStERFRP5s6dC4lEgkWLFj3voZCWvPHGG5BIJPjtt9/qbZtqBRYDAwPIZDIkJCQotCckJKBnz54q13Fzc1Pqv3//fri6ukJfXx+Ojo64cOECzp07J1/eeust9OvXD+fOnaty5sTQ0BDNmzdXWIiISPtsbW0hkUiUliZNmsDZ2RkfffQR7t69q3Ld27dvY+nSpbCwsMCUKVMUXouNjVVZ9+nlwIED9fE21bZ9+3ZIJBLo6Ojgr7/+qrJfaWkpvL29IZFI0KxZM7VOf6hrCQkJGDFiBOzs7CCVSmFkZIR27dphzJgxOHLkSJXrzZ8/HwAwc+ZMlJeX18tY1TqHBQCCgoIwduxYuLq6ws3NDatWrUJaWhr8/f0BVMx8pKenY926dQAAf39/fPfddwgKCsJ7772HxMRExMTEYPPmzQAAqVQKFxcXhW20aNECAJTaiYiofuXk5MhnsE1NTWFgYACg4kM4JycHly9fxuXLlxEXF4fExESlPzJDQkLw6NEjhIeHo2nTpiq3oaOjAwsLiyrHYGhoqKV3o11Dhw6Fs7MzLl26hIiICGzYsEFlvylTpmDv3r3Q09PD1q1b0bVr1/odqAqCIGDy5MlYuXKlvE0qlUIikSAlJQUpKSnYtGkTZsyYgaVLlyqt36NHD3h5eWHfvn3YsGEDxo0bV+djVvsclpEjRyIyMhLh4eHo2rUrfv/9d8THx8POzg4AkJGRoXBPlrZt2yI+Ph6HDx9G165dsWDBAixbtgzDhg3T3rsgIqI6kZSUJP/3oUOHkJmZiczMTGRnZ+PevXvyP1bT09MREhKisG56ejo2btwIAwMDTJw4scpt2NjYyOuqWsR6by6JRII5c+YAqLjpqapTGCIiIrBq1SoAFTddfeONN+p1jFWJjY2Vh5Xhw4fj6tWrePToER4+fIi///4bgwYNAgB8/fXX2LFjh8oalT/7+jrUp9FJtwEBAUhNTUVRURGSkpLQu3dv+WuxsbE4fPiwQv8+ffrg7NmzKCoqQkpKivxNViU2NhY///yzJkMjIiItqgws+vr6cHJyUnjN1NQU33//PV566SUAQHx8vMLr0dHRKCsrg4+PD1q2bFk/A9ZQeXk5Dh06hJs3b6q13qhRo+Dg4ICysjJ8+eWXCq9t3rxZHuLmzJmD9957T2vjfZq64688CtK+fXts3rwZHTp0kL/WsWNHbN26VX5PtB9//FFljcqf619//YXjx4/X8h08G58lREREVTp79iwAwNnZWX446Ek6Ojro3r07gIrDR2VlZQAqDjnExMQAAHx9fetptOq7dOkSgoODYW9vj//9739ISUlRa31dXV3Mnj0bALB27Vrcvn0bAHD06FFMmDABgiDA19cXn332mdbHDmg+/oyMDABAly5doKenfHaIvr6+/NBVQUGByhoGBgbyoyWVs0h1iYGFiIiqVDnD0qVLlyr7FBcXAwCMjY2hq6sLALh48aL8w1tsh3SysrLwzTffwNXVFS+99BK++OIL3Lp1C6amphrNBI0fPx42NjYoLi7GkiVLcOXKFQwePBhFRUXo06cPfvjhh2pv/fE8xl85e3L+/HmUlpYqvV5SUiI/OdjV1bXKOpVHWPbu3avmu1AfAwsREal0//59+V/sVQUWQRCQmJgIAHj55Zfl7b///juAivNTWrVqVe127t69C5lMBmNjY/lVKu+8847S6QW18ejRI2zZsgVvvvkmrK2tERgYiKSkJEilUgwfPhw7duxAZmYmOnfurHZtfX19zJo1C0DFYTBvb2/cu3cPTk5O2LFjh8qZqec9/smTJwMArl27htGjR+PatWvy165cuYIRI0bgxo0bcHBwwIwZM6qs8+qrrwKoCFF///13Ld7hs6l9lRAREf03VB4OAlDllS0rV66Uh5rx48fL20+dOgWg+pmZSg8fPsTZs2dhamqKwsJC+VUqGzduxIQJE7Bq1SqVhy2eRRAEHDlyBOvXr8e2bdvkd0TX0dHB//73P4wZMwbDhw/Xym0x/Pz88PnnnyMzMxMpKSmwtLREfHw8TE1NNa5Zl+MfOHAgvv76a3zyySfYtm0btm3bBiMjIwAV4ahFixaYPHkyPvvss2rrd+jQAcbGxigoKEBiYiIcHR01e7M1wMBCREQqPRlYngwexcXF+Oeff7BmzRpERkYCAP73v/8pBJY7d+4AQLWXK1tZWSE0NBRDhw5Fx44dYWhoiLKyMpw6dQqhoaE4cOAAfvjhBzRt2hTffvttjcd9+fJlrF+/Hhs3blS4arVr16545513MHr0aFhZWdW4Xk3o6+ujffv28hulrl+/Hvb29hrVqq/xBwYGokOHDpg4cSKysrLw6NEj+WtFRUXIz89Hbm7uMw8zmZmZoaCgQP4zrysMLEREpNKTlzRX9+gUX19frFy5Un7+CgD5jeSq+7Dz9PRUejiurq4uevbsiX379mHo0KH45ZdfsHz5ckybNk3hSpaqxMXFYdSoUfKv7e3t4evrizFjxsDZ2fmZ62tq6tSpOHbsmPzro0ePwsPDQ+069TX+hw8fYsKECfjxxx/h6uqKDRs24OWXX4YgCEhOTsacOXOwYcMG7N27FwcPHqz2UFPLli1x8+bNKm8eqC08h4WIiFSqnGFp0qQJLC0tYWlpiVatWqF9+/Zwd3fHzJkzkZycjI0bN8LY2Fhh3cePHwPQ/KZvOjo6WLJkCYCKS3Z37txZo/WenCUwMjLCiBEjMGrUqDoNKxEREYiKigJQcXd3APj22281eihvfY3/448/xo8//ogXX3wRv//+Ozw8PGBmZgZzc3N4eHjg999/x4svvojs7GylOxQ/rfJQUuXPvK4wsBARkZK8vDz5iZjz58+X38QtIyMD//zzD37//XcsXry4ynNbzMzMAFScuKup9u3by2d2bty4UaN1vL29ERYWhg4dOuDRo0dYtGgROnfujE6dOuGLL75Q+z4rz7Jx40b5vVY+/fRT7Ny5E8bGxnjw4AGWL1+udr36GH9+fr78MuSpU6fKA8eTjIyMMHXqVADAsWPHkJWVVWW9e/fuAfi/n3ldYWAhIiIlycnJEAQBQPWXtVal8tyVyg+z+mJpaYlPP/0UV69eRWJiIgICAmBmZoaLFy8iODgYbdu2hbu7O6KiopCTk1Orbf3222+YOHEiBEHA+PHjERYWBjMzM/nNUb/++muFGROxjP/q1avyS5kdHByq7PfkIbjq7u9S+TOu7nwlbWBgISIiJZWHgyQSicLlyjVVeQijpjMjqly/fh3Z2dkAKh7zoq4ePXrg+++/R0ZGBnbs2IGhQ4fCwMAAx44dw+TJk9G6dWsMHDgQW7ZswcOHD9WqffHiRQwdOhTFxcXw8PBAdHS0/LWZM2dCKpUiKytLoV0s49fR+b+P/upmbP7991/5v5s1a6ayT35+vvxn9PSdkLWNgYWIiJRUnnDr4OAAExMTtdevvKHY+fPnUVRUpPR65exNVQRBwMcffwyg4gN2wIABao+hkr6+PgYPHozt27cjIyMDUVFR6NWrF0pKSrBr1y6MHj0alpaWGDt2bI2udElPT4e3tzdyc3PRpUsXbNu2Dfr6+vLXLS0t4efnBwBYvHix/MZ6Yhm/o6Oj/DDQ6tWrVd44rqysTH7YyNTUFB07dlRZ68yZMygvL4eenh569epVi3f5bAwsRESkpHKGRZPDQQDQq1cv6Onpobi4WH7H1CfdvHkTr7zyClauXIkbN27IA0x5eTlOnjwJb29v+UP3Pvjggyo/MNVlamqKDz74AMeOHcP169cxf/58tG/fHgUFBdiwYQOuXr1a7fp5eXnw8fHB7du3YWNjg927d6u8T8knn3wCAwMD3L59W/7cHjGMH6g4P6UyUJ09exYDBw7EhQsXUF5ejvLycvz555/w8fHBiRMnAFRc/vzkFWBPqrzfzssvv6x04rW2MbAQEZGCwsJCXLlyBQAgk8k0qtG8eXO8+eabAIBff/1VZZ8//vgD/v7+cHBwgJGRESwsLNCkSRO4ublh3759AIAJEyZg2bJlGo3hWdq1a4fQ0FD8888/OHHiBCZPnlzth25JSQmGDh2KP//8EyYmJoiPj4e1tbXKvm3atMG4ceMAAF988YX8GUvPc/xP+vLLL+VPjt67dy86d+6MJk2aoEmTJujSpQv2798PABg9erTSU7ifVPmzrY/nRTGwEBGRgnPnzqG8vByA5oEFqJgZAYBNmzYpHQKytLTEt99+C19fXzg7O6N58+Z48OAB9PX14ejoiIkTJ+LYsWNYs2aNRne5VZebmxuWL19e7YzSpEmTcPDgQejr6+Onn36Ci4tLtTWDg4Ohp6eH69evIy4uTttDVlCT8T/JyMgI8fHx2Lp1KwYNGoQ2bdrIf0Y2NjYYNmwYdu3ahU2bNlU5u5KSkoLExEQYGRnJw1ld4o3jiIhIQa9evZ55jklNeHl5wcHBAdevX8fRo0fl57UA/3fZbOWlsw3BunXr1Dq8065dO5SUlNThiGpHIpFg+PDhGD58uEbrr1+/HgAwatSoWj2CoKY4w0JERHVCR0cHCxYsAFBxWIQaj8LCQnz77bcwNDREaGhovWyTgYWIiOrMqFGj8Morr2DPnj3yEzSp4fvuu++QnZ2NadOmwc7Orl62yUNCRERUZyQSCVauXImff/5Zfr8OaviaNm2K+fPnIzAwsN62ycBCRER1qmvXrlXewp8apudx7hEPCREREZHoMbAQERGR6DGwEBERkegxsBAREZHoMbAQERGR6DGwEBGRxvLz8zF//nx06tQJxsbGMDExQffu3fHVV1/V6inFDx48wC+//IJPP/0UAwYMQOvWrSGRSCCRSBAbG6txXW9vb3mdvn37alyH6h8vayYi+o8ICwvTSp3KO5vevHkTffv2RWpqKgCgSZMmKCoqwpkzZ3DmzBls3LgRBw8e1Oi27T///DMmTJiglfFWio2Nxd69e7Vak+oPZ1iIiEhtZWVlGDhwIFJTU9G6dWskJCSgsLAQDx8+xJYtW9CsWTMkJydjzJgxGm+jVatW8Pb2RkhICLZv316r8WZmZiIoKAgtWrSAk5NTrWrR88EZFiIiUltsbCwuXLgAANi+fTvc3NwAVDw/aOTIkSgvL4evry/27NmDgwcP4vXXX1er/jvvvIN3331Xa+MNCAjA/fv3ER0djQ0bNuDy5ctaq031g4GF6oW2p6KJ6Plau3YtAKBfv37ysPKkUaNGISQkBCkpKVi3bp3agUVPT3sfTz/++CN27NiBPn36YNKkSdiwYYPWalP94SEhIiJSy8OHD3H8+HEAFSexqiKRSPDGG28AAPbv319vY3taTk4OPvzwQxgaGmLVqlWQSCTPbSxUOwwsRESklsuXL6O8vBwA4OLiUmW/ytcyMzNx7969ehnb06ZNm4asrCzMmzcPL7744nMZA2kHAwsREanlzp078n9bW1tX2e/J155cp77s3LkTmzZtgouLC2bNmlXv2yftYmAhIiK15Ofny//dpEmTKvs9+dqT69SH3NxcTJ48GTo6OoiOjoa+vn69bp+0j4GFiIganY8++gjp6ekICAhAjx49nvdwSAsYWIiISC3NmjWT//vhw4dV9nvytSfXqWsHDhxATEwM2rRpg4ULF9bbdqluMbAQEZFarKys5P9OT0+vst+Trz25Tl177733AACLFi2CRCJBQUGBwlJWVgag4uZ3T7eReDGwEBGRWpycnKCjU/HxcfHixSr7Vb7WqlUrtGzZsl7GBkD+qABfX180a9ZMaTl27BgA4NixY/K2nTt31tv4SDMaBZbly5ejbdu2kEqlkMlkOHr0aLX9jxw5AplMBqlUinbt2iEqKkrh9ejoaLi7u8PU1BSmpqbo378/Tp8+rcnQiIiojjVp0gS9evUCgCqfzSMIAvbt2wcA8PT0rLexUeOldmCJi4tDYGAgQkJCkJycDHd3d3h7eyMtLU1l/5SUFPj4+MDd3R3JycmYM2cOpk2bpvBciMOHD2P06NE4dOgQEhMTYWtrC09Pz2qnGomI6PkZP348AODQoUM4deqU0utbt27FjRs3AADjxo2r17EJglDt0qdPHwBAnz595G2DBw+u1zGS+tQOLEuXLsWkSZPg5+cHJycnREZGwsbGBitWrFDZPyoqCra2toiMjISTkxP8/PwwceJELFmyRN5n48aNCAgIQNeuXeHo6Ijo6GiUl5fj4MGDmr8zIiKqM+PHj0enTp0gCAKGDRsm/31dXl6OrVu3ys8j8fb2Vnlb/vnz50MikUAikcgP4TwtOztbYalUUFCg0F7dib/UeKgVWIqLi5GUlKQ0vefp6YkTJ06oXCcxMVGpv5eXF86cOYOSkhKV6zx8+BAlJSX1esyTiIhqTk9PD7/++ivs7e2Rnp6O/v37o2nTpmjatClGjBiBvLw8dOvWDRs3btR4GxYWFgpLpQ8//FChfdGiRdp4SyRyagWW7OxslJWVwdLSUqHd0tISmZmZKtfJzMxU2b+0tFQhMT9p9uzZsLa2Rv/+/ascS1FREfLy8hQWIiKqP/b29vjzzz/x6aefwsXFBRKJBPr6+pDJZFiyZAlOnjwJU1PT5z1MaiQ0ehzm0w+PEgSh2gdKqeqvqh2ouAxt8+bNOHz4MKRSaZU1IyIitPYEYCIi0kyzZs0QFham9u/j+fPnY/78+dX2qfys0LbDhw/XSV2qW2rNsJibm0NXV1dpNiUrK0tpFqVSq1atVPbX09ODmZmZQvuSJUuwcOFC7N+/H507d652LMHBwcjNzZUvt27dUuetEBERUQOiVmAxMDCATCZDQkKCQntCQgJ69uypch03Nzel/vv374erq6vCsx0WL16MBQsWYO/evXB1dX3mWAwNDdG8eXOFhYiIiBonta8SCgoKwurVq7FmzRpcvnwZM2bMQFpaGvz9/QFUzHw8eQmbv78/bt68iaCgIFy+fBlr1qxBTEwMZs6cKe+zaNEizJ07F2vWrIG9vT0yMzORmZmJgoICLbxFIiIiaujUPodl5MiRyMnJQXh4ODIyMuDi4oL4+HjY2dkBADIyMhTuydK2bVvEx8djxowZ+P7772FlZYVly5Zh2LBh8j7Lly9HcXExhg8frrCt0NDQZx7jJCIiosZPo5NuAwICEBAQoPK12NhYpbY+ffrg7NmzVdar6hp8IiIiIoDPEiIiIqIGgIGFiIiIRI+BhYiIiESPgYWIiIhEj4GFiIiIRI+BhYiIiESPgYWIiIhEj4GFiIiIRE+jG8cRERFVUvdJzVUJDQ3VSh1qnDjDQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESixxvHkQLeAIqIiMSIMyxEREQkegwsREREJHoMLERERCR6DCxEREQkegwsREREJHoMLERERCR6DCxEREQkegwsREREJHq8cRwREYkWb2ZJlTjDQkRERKLHwEJERESix8BCREREosfAQkRERKLHwEJERESix8BCREREosfAQkRERKLH+7A0QLwvARER/dcwsBAR0X8S//hrWHhIiIiIiERPo8CyfPlytG3bFlKpFDKZDEePHq22/5EjRyCTySCVStGuXTtERUUp9dm+fTucnZ1haGgIZ2dn7NixQ5OhERERUSOkdmCJi4tDYGAgQkJCkJycDHd3d3h7eyMtLU1l/5SUFPj4+MDd3R3JycmYM2cOpk2bhu3bt8v7JCYmYuTIkRg7dizOnz+PsWPHYsSIETh16pTm74yIiIgaDbXPYVm6dCkmTZoEPz8/AEBkZCT27duHFStWICIiQql/VFQUbG1tERkZCQBwcnLCmTNnsGTJEgwbNkxew8PDA8HBwQCA4OBgHDlyBJGRkdi8ebOm742IiKje8dyYuqFWYCkuLkZSUhJmz56t0O7p6YkTJ06oXCcxMRGenp4KbV5eXoiJiUFJSQn09fWRmJiIGTNmKPWpDDmqFBUVoaioSP51bm4uACAvL0+dt1SnVAU4TVQGuUqPHz/WSl1V36u6ql2XY87XSmUgD/VXmz9DRRxz3dety9oNccx1Wbsux1xXnyvPU+X7FASh+o6CGtLT0wUAwvHjxxXaP//8c+HFF19UuU6HDh2Ezz//XKHt+PHjAgDhzp07giAIgr6+vrBx40aFPhs3bhQMDAyqHEtoaKgAgAsXLly4cOHSCJZbt25Vm0E0uqxZIpEofC0IglLbs/o/3a5uzeDgYAQFBcm/fvDgAezs7JCWlgYTE5Nnv4kaysvLg42NDW7duoXmzZtrrW5d1uaYG35tjrl+anPM9VO7IY65LmtzzIoEQUB+fj6srKyq7adWYDE3N4euri4yMzMV2rOysmBpaalynVatWqnsr6enBzMzs2r7VFUTAAwNDWFoaKjUbmJiovVvJgA0b968TurWZW2OueHX5pjrpzbHXD+1G+KY67I2x/x/ajLRoNZVQgYGBpDJZEhISFBoT0hIQM+ePVWu4+bmptR///79cHV1hb6+frV9qqpJRERE/y1qHxIKCgrC2LFj4erqCjc3N6xatQppaWnw9/cHUHGoJj09HevWrQMA+Pv747vvvkNQUBDee+89JCYmIiYmRuHqn+nTp6N379748ssvMWjQIPzyyy84cOAAjh07pqW3SURERA2Z2oFl5MiRyMnJQXh4ODIyMuDi4oL4+HjY2dkBADIyMhTuydK2bVvEx8djxowZ+P7772FlZYVly5bJL2kGgJ49e2LLli2YO3cu5s2bBwcHB8TFxeHVV1+t8bgMDQ0RGhqq8jBRbdRV3bqszTE3/Nocc/3U5pjrp3ZDHHNd1uaYNSMRhGddR0RERET0fPFZQkRERCR6DCxEREQkegwsREREJHoNPrAUFBQgMDAQVlZWkEql6Nq1K7Zs2VLruvn5+Zg1axY8PT1hYWEBiUSC+fPn17rub7/9hokTJ8LR0RFNmzaFtbU1Bg0ahKSkpFrVPXfuHN58803Y2trCyMgILVu2hJubGzZs2FDrMT9t9erVkEgkMDY2rlWdw4cPQyKRqFxOnjyplbEeO3YMPj4+MDU1hZGRETp06IAFCxbUqua7775b5bhrO/bk5GQMHjwYVlZWaNKkCRwdHREeHo6HDx/WasynT5+Gl5cXmjVrBmNjY/Tr1w/Hjx9Xq4Y6+8TZs2fRv39/GBsbo0WLFhg6dChu3LhR69rHjh2Dn58fZDIZDA0NIZFIkJqaWutxl5WVYenSpXjjjTfQpk0bNGnSBE5OTpg9ezYePHhQqzEvW7YMPXr0gLm5OQwNDWFra4tRo0bhr7/+qvX340mCIKB3796QSCSYOnVqrepW9X/c0dFRK2MuKSnB0qVL0alTJxgZGaFFixbo2bOnyke81LRudftkVeOuaW1BEBAdHQ2ZTIbmzZvDzMwMffr0we7du2tdd9myZXB0dIShoSFat26NyZMn4/79+yrrqvP5oe4+WNPamuyD2tLgA8vQoUOxdu1ahIaGYs+ePejevTtGjx6NTZs21apuTk4OVq1ahaKiIgwePFg7gwWwYsUKpKamYvr06YiPj8c333yDrKws9OjRA7/99pvGdR88eAAbGxssXLgQ8fHxWLduHezt7TF27Fh89tlnWht/eno6Zs6c+cw7Eqpj4cKFSExMVFhcXFxqXXfTpk3o06cPTExMsG7dOsTHx+OTTz559vMqnmHevHlK401MTIS5uTmsra3RvXt3jepeunQJPXv2RGpqKiIjI7Fr1y6MGjUK4eHhGD16tMbj/eOPP9C7d288evQI69evx/r16/H48WO8/vrrSExMrHGdmu4Tf//9N/r27Yvi4mL8+OOPWLNmDa5evQp3d3fcvXu3VrUPHjyIAwcOwNbWtsb3aapJ7UePHmH+/Pmws7NDZGQk4uPj8d5772HVqlXo1asXHj16pPGYc3Jy4O3tjdWrV2P//v0ICwtDcnIyXn31VVy5ckXjMT/t+++/x7Vr16rto05dIyMjpf/jcXFxta5dVlaGIUOGyP9f79mzBxs3bsQbb7yBwsJCjeuq2icrn0c3ZMiQWo05NDQU77//Pl555RVs374dsbGxMDQ0xIABA/DTTz9pXHfmzJmYMWMGBg0ahF27dmH27NnYtGkTPDw8UFJSotS/pp8fmuyDNa2tyT6oNdXeuF/kdu/eLQAQNm3apNDu4eEhWFlZCaWlpRrXLi8vF8rLywVBEIS7d+8KAITQ0NDaDFcQBEH4999/ldry8/MFS0tL4fXXX691/ae9+uqrgo2NjdbqDRgwQBg4cKAwfvx4oWnTprWqdejQIQGAsHXrVi2N7v/cvn1baNq0qTB58mSt11bl8OHDAgBh7ty5GtcICQkRAAjXrl1TaH///fcFAMK9e/c0quvl5SVYWloKhYWF8ra8vDzB3Nxc6NmzZ43r1HSfePvttwVzc3MhNzdX3paamiro6+sLs2bNqlXtsrIy+b8XL14sABBSUlJqPe7S0lIhOztbad2tW7cKAIT169drPGZVLl26JAAQ5s2bp/GYn5SSkiIYGxsLP/30kwBAmDJlSq3qarJ/17T2119/Lejo6AiJiYlaravKu+++K0gkEuGff/6pVW1ra2vhtddeU2h79OiRYGJiIrz11lsa1b19+7agq6srfPjhhwrtmzZtEgAIq1atUqpb088PTfbBmtbWZB/UlgY9w7Jjxw4YGxvj7bffVmifMGEC7ty5g1OnTmlcu3IqUdteeOEFpTZjY2M4Ozvj1q1bWt+eubk59PQ0emSUkg0bNuDIkSNYvny5VurVpdWrV6OwsBCffPJJvWwvJiYGEokEEydO1LhG5Z2fn75FdYsWLaCjowMDAwON6h4/fhx9+/ZFkyZN5G3NmjVD7969ceLECWRkZNSoTk32idLSUuzatQvDhg1TuH23nZ0d+vXrhx07dmhcGwB0dNT/lVWT2rq6uvJHhTzplVdeAQCV+2ZtfkdYWFgAQJX7prq133//fXh4eFQ5k6BpXXXUtPY333yD3r17o0ePHlqt+7T8/Hxs3boVffr0Qfv27WtVW19fX2m/lEql8kWTuidPnkRZWRl8fHwU2gcMGAAA2L59u9I6Nfn80HQfrOlnkyb7oLY06MBy8eJFODk5Ke30nTt3lr/eEOTm5uLs2bN46aWXal2rvLwcpaWluHv3LpYvX459+/Zp5UM7KysLgYGB+OKLL9CmTZta13vSlClToKenh+bNm8PLy0srdzj+/fff0bJlS/z999/o2rUr9PT08MILL8Df31/lI9trIzc3F9u2bcPrr7+Otm3balxn/PjxaNGiBSZPnowbN24gPz8fu3btwsqVKzFlyhQ0bdpUo7rFxcUqb/ZU2XbhwgWNx/y069ev49GjR/J98EmdO3fGtWvX8PjxY61tr65VToVrY98sKytDUVER/v77b/j5+eGFF17AhAkTal139erVOH36NL777rta13rSo0eP0KpVK+jq6qJNmzaYOnUq7t27V6uat27dQmpqKjp16oQ5c+bA0tISenp6eOmll7B27VotjbzCli1bUFhYCD8/v1rXmj59Ovbu3YuYmBjcv38fGRkZCAoKQm5uLqZNm6ZRzeLiYgBQ2jf19fUhkUjw559/1qjO058f2twHtfnZpA3a+dP7OcnJyUG7du2U2lu2bCl/vSGYMmUKCgsLERISUutaAQEBWLlyJYCKZz8tW7YMH3zwgVbqduzYEZMnT651rUomJiaYPn06+vbtCzMzM1y7dg2LFy9G3759sXv3bnh5eWlcOz09HQ8fPsTbb7+N4OBgREZG4o8//kBoaCguXryIo0ePau0vzc2bN+PRo0eYNGlSrerY29sjMTERQ4YMgYODg7x92rRp8mPxmnB2dsbJkydRXl4u/+uotLRUPgOpzf2kslblPvikli1bQhAE3L9/H61bt9baNutKeno6Zs+eDVdXV/lfvbXRtGlTFBUVAQBefPFFHD58GDY2NrUe48yZM7Fo0SKtnlfWpUsXdOnSRX4u2ZEjR/D111/j4MGD+OOPPzQ+4T49PR0AsHbtWrRp0wbfffcdTExMEB0djXfffRfFxcV47733tPIeYmJi0KJFC4W7qmsqMDAQRkZGmDJlijwAtWzZEjt37kSvXr00quns7AygYga0X79+8vYTJ05AEIQa75dPf35ocx/U5meTNjTowAKg2g+dupr61KZ58+Zh48aN+PbbbyGTyWpdb86cOfDz80NWVhZ27tyJqVOnorCwEDNnztS45vbt27Fz504kJydr9XvarVs3dOvWTf61u7s7hgwZgk6dOmHWrFm1Cizl5eV4/PgxQkNDMXv2bABA3759YWBggMDAQBw8eBD9+/ev9XsAKn4xmpmZPXM6/llSU1MxcOBAWFpaYtu2bbCwsMCpU6fw2WefoaCgADExMRrV/fDDDzFp0iRMnToVISEhKC8vR1hYGG7evAmgbqZ4G/p+ee/ePfj4+EAQBMTFxWnle3TixAkUFxfj+vXr+Prrr9GvXz8cPHiwVn+9+vv7o0uXLlr7kK80Y8YMha89PDzQrVs3DB8+HNHR0Uqv11R5eTkA4PHjxwqPdPHw8ICrqyvCw8O18l7++usvnDp1ClOmTFF5yEZdP/zwA6ZPn46pU6fC29sbxcXFWLduHQYNGoSffvpJo99VXbp0Qe/evbF48WJ07NgRHh4euHTpEvz9/aGrq1uj/3PVfX7Udh/U9meTNjToQ0JmZmYqU2jltKWqhCkmYWFh+Oyzz/D5559XeRmiumxtbeHq6gofHx+sWLEC77//PoKDg6s8M/xZCgoKMGXKFHz44YewsrLCgwcP8ODBA/l05oMHD1Se2a+pFi1aYMCAAfjzzz9VXplRU5XnIzz9i8Tb2xtAxSV/2vDnn3/izJkzeOedd2r9jI3Zs2cjLy8P+/btw7Bhw9C7d298/PHHiIyMxJo1a3DkyBGN6k6cOBFffPEF1q9fjzZt2sDW1haXLl2Sh1hra+tajftJld/3qvZLiUSCFi1aaG17deH+/fvw8PBAeno6EhISVM7iauLll19Gjx49MGbMGBw6dAiCIGDOnDka19u2bRv27t2LRYsWITc3V75vAhWHGx48eKDyShNNDRkyBE2bNq3VZfuV/z8cHR3lYQWo+AD18vLC7du3kZWVVeuxVoZ7bRwOun//vnxmZcmSJXj99dfh7e2NzZs3o3v37vIH/2pi69at6NWrF0aMGAFTU1P069cPQ4cORdeuXZ+5X1b1+aGNfbAuPpu0oUEHlk6dOuHy5csoLS1VaK88Jq+NS2PrSlhYGObPn4/58+fX6pfWs7zyyisoLS2t9vr76mRnZ+Pff//FV199BVNTU/myefNmFBYWwtTUFGPGjNHqmIX/f9lxbf4SV3X89sna2ppV0OYvxnPnzsHZ2VnpXJXKy6Rrc07WJ598guzsbFy4cAGpqak4ceIE7t+/j6ZNm2r1rycHBwcYGRmpPC/mwoULaN++vVb+4q0r9+/fR//+/ZGSkoKEhIQq/x/VVrNmzeDo6IirV69qXOPixYsoLS1Fjx49FPZNAIiOjoapqWmV9wnRlCAItdp3HBwcFE7+fro2UPt9s7i4GOvXr4dMJkPXrl1rVQsArly5gkePHqm8XYGrqytSU1NRUFCgUe0XXngB8fHx+Pfff3H+/HlkZWUhPDwcV69eRe/evatcr7rPj9rug/X12aSJBh1YhgwZgoKCAqWzqdeuXQsrKyu1nvZcnxYsWID58+dj7ty5CA0NrdNtHTp0CDo6Ohr/ldiqVSscOnRIafHy8oJUKsWhQ4e0ep+X+/fvY9euXejatWutPtgqj1vv2bNHoT0+Ph4AanyFQnWKioqwYcMGvPLKK1oJx1ZWVvjrr7+UfvlV3iultic7GxoawsXFBXZ2dkhLS0NcXBzee+89GBkZ1aruk/T09DBw4ED89NNPyM/Pl7enpaXh0KFDGDp0qNa2pW2VYeXGjRvYv3+/wuFKbasMj1VdvVIT7777rsp9EwAGDx6MQ4cO4bXXXtPWkLFt2zY8fPiwVvuOnp4eBg0ahMuXLyvcbEwQBOzduxcODg4wNzev1Th//fVXZGdn1/qcskqV5wY9PbMkCAJOnjwJU1NTjU+Ir/TCCy+gc+fOMDExQVRUFAoLC6uc2XjW50dt9sH6/GzSRIM+h8Xb2xseHh6YPHky8vLy0L59e2zevBl79+7Fhg0boKurW6v6e/bsQWFhofyHfunSJWzbtg0A4OPjU+VfCtX56quv8Omnn+KNN97Am2++qbQTaPrL4P3330fz5s3xyiuvwNLSEtnZ2di6dSvi4uLw8ccfyy+jVJdUKkXfvn2V2mNjY6Grq6vytZry9fWVH8IyNzfHP//8g6+++gr//vsvYmNjNa4LAJ6enhg4cCDCw8NRXl6OHj164MyZMwgLC8OAAQO08ov8559/xr1797QyuwJUnNg3ePBgeHh4YMaMGTA3N8fJkycREREBZ2dn+eEsdV28eBHbt2+Hq6srDA0Ncf78eXzxxRca3fW3JvtEWFgYunfvjgEDBmD27Nl4/PgxPv30U5ibm+Ojjz6qVe27d+/KD41V/gW5Z88eWFhYwMLCAn369NGoduUhieTkZERGRqK0tFRh37SwsFA4EbqmdUtKSuDh4QFfX1906NABRkZGuHr1Kr755hsUFRVV+6HwrNr29vawt7dXua61tXWV++az6t69exe+vr4YNWoU2rdvD4lEgiNHjiAyMhIvvfRStf/fa/IzXLBgAfbs2YM33ngD8+fPR/PmzbF69WqcP38eP/74o8Z1K8XExMDIyAi+vr5VjlOd2ra2thg6dChWrVoFQ0ND+Pj4oKioCGvXrsXx48exYMEClbPBNRlzdHQ0gIpZkQcPHmDPnj2IiYnBwoUL8fLLLyvVrOnnhyb7YE1ra7oPakW93O2lDuXn5wvTpk0TWrVqJRgYGAidO3cWNm/erJXadnZ2AgCVi6Y3yunTp0+VNWvz41izZo3g7u4umJubC3p6ekKLFi2EPn36qLzhlTZo48ZxERERQteuXQUTExNBV1dXsLCwEIYMGSKcPn1aK2N8+PCh8Mknnwg2NjaCnp6eYGtrKwQHBwuPHz/WSn0PDw+hadOmQl5enlbqCYIg/Pbbb4Knp6fQqlUrwcjISHjxxReFjz76SOVNzWrqypUrQu/evYWWLVsKBgYGQvv27YW5c+cKBQUFateq6T5x5swZ4fXXXxeaNGkiNG/eXBg8eLDSDfE0qV15s0FVS58+fTSunZKSUu1+OX78eI3qPn78WPDz8xOcnJwEY2NjQU9PT2jTpo3wzjvvCH/99ZdWvtdPQzU3jqtJ3Xv37glDhgwR7O3tBSMjI8HAwEDo0KGDMGvWLOHBgwdaGfOFCxeEN998U2jWrJkglUqFHj16CDt37qx13bS0NEFHR0cYN25cteNUt/ajR4+ExYsXC507dxaaNWsmtGzZUujRo4ewYcMG+Q3iNKm7cuVKwcnJSWjSpIlgbGwsuLu7Cz///HOVY1Xn80PdfbCmtTXdB7VBIgi1vE85ERERUR1r0OewEBER0X8DAwsRERGJHgMLERERiR4DCxEREYkeAwsRERGJHgMLERERiR4DCxEREYkeAwsRERGJHgMLERERiR4DCxEREYkeAwsRERGJHgMLERERid7/A2SrInkGZBBTAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X+1))\n",
    "x2 = list(np.arange(X+1,Y))\n",
    "x3 = list(np.arange(Y,22))\n",
    "plt.bar(x1, hypergeom.pmf(x1, n = m, M = N, N = n), color ='gray')\n",
    "plt.bar(x2, hypergeom.pmf(x2, n = m, M = N, N = n), color ='#DFFF00')\n",
    "plt.bar(x3, hypergeom.pmf(x3, n = m, M = N, N = n), color ='gray')\n",
    "plt.xlim(0,22)\n",
    "plt.xticks(np.arange(0,22), fontsize=12, ha='center')\n",
    "plt.title(f'$HG{N,m,n}$')\n",
    "xs = np.arange(X+1, Y)\n",
    "prob = np.sum([hypergeom.pmf(xs, n = m, M = N, N = n) for xs in xs])\n",
    "plt.text(15, 0.02, f'$P({np.round(X, 3)} < X < {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "xwTO30WBoQCh"
   },
   "source": [
    "To find the probability between two points $[X,Y)$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "t6Acq0cAoQCj",
    "outputId": "f32a86f9-c1d7-4252-cdcb-b6b1044e9726"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *[5, 8)* in the HG(500, 50, 100) Distribution is:  0.1623105533635753\n"
     ]
    }
   ],
   "source": [
    "X = 5\n",
    "Y = 8\n",
    "m, N, n = [50, 500, 100]\n",
    "xs = np.arange(X, Y)\n",
    "print(f'The probability between *[{X}, {Y})* in the HG{N,m,n} Distribution is: ', np.sum([hypergeom.pmf(xs, n = m, M = N, N = n) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "id": "4hoRiuhXoQCk",
    "outputId": "4abeab49-b4a5-4fb2-9fcf-00f62b7aa14e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X))\n",
    "x2 = list(np.arange(X,Y))\n",
    "x3 = list(np.arange(Y,22))\n",
    "plt.bar(x1, hypergeom.pmf(x1, n = m, M = N, N = n), color ='gray')\n",
    "plt.bar(x2, hypergeom.pmf(x2, n = m, M = N, N = n), color ='#DFFF00')\n",
    "plt.bar(x3, hypergeom.pmf(x3, n = m, M = N, N = n), color ='gray')\n",
    "plt.xlim(0,22)\n",
    "plt.xticks(np.arange(0,22), fontsize=12, ha='center')\n",
    "plt.title(f'$HG{N,m,n}$')\n",
    "xs = np.arange(X, Y)\n",
    "prob = np.sum([hypergeom.pmf(xs, n = m, M = N, N = n) for xs in xs])\n",
    "plt.text(15, 0.02, f'$P({np.round(X, 3)} \\leq X < {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mcOv4nPnoxCs"
   },
   "source": [
    "To find the probability between two points $(X,Y]$ use the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "_TK4upMwoxCt",
    "outputId": "93eb8b12-f250-4a28-966e-c2872c2ce908"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability between *(5, 8]* in the HG(500, 50, 100) Distribution is:  0.25550294432987475\n"
     ]
    }
   ],
   "source": [
    "X = 5\n",
    "Y = 8\n",
    "m, N, n = [50, 500, 100]\n",
    "xs = np.arange(X+1, Y+1)\n",
    "print(f'The probability between *({X}, {Y}]* in the HG{N,m,n} Distribution is: ', np.sum([hypergeom.pmf(xs, n = m, M = N, N = n) for xs in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "id": "HWTyiIjcoxCu",
    "outputId": "f405c9c5-2029-4056-a96b-08a0c246bbd6"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X+1))\n",
    "x2 = list(np.arange(X+1,Y+1))\n",
    "x3 = list(np.arange(Y+1,22))\n",
    "plt.bar(x1, hypergeom.pmf(x1, n = m, M = N, N = n), color ='gray')\n",
    "plt.bar(x2, hypergeom.pmf(x2, n = m, M = N, N = n), color ='#DFFF00')\n",
    "plt.bar(x3, hypergeom.pmf(x3, n = m, M = N, N = n), color ='gray')\n",
    "plt.xlim(0,22)\n",
    "plt.xticks(np.arange(0,22), fontsize=12, ha='center')\n",
    "plt.title(f'$HG{N,m,n}$')\n",
    "xs = np.arange(X+1, Y+1)\n",
    "prob = np.sum([hypergeom.pmf(xs, n = m, M = N, N = n) for xs in xs])\n",
    "plt.text(15, 0.02, f'$P({np.round(X, 3)} < X \\leq {np.round(Y, 3)})$ \\n {np.round(prob, 2)}', fontsize=18);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "W-YEA62apQdT"
   },
   "source": [
    "To find the probability of a point use the code below:\n",
    "\n",
    "''\n",
    "hypergeom.pmf(X, n = m, M = N, N = n)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Vjbq7iqgpQdT",
    "outputId": "595cfe62-ef00-406d-b32a-aecb8b653a24"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability of *X=7* in the HG(500, 50, 100) Distribution is:  0.08515328996154319\n"
     ]
    }
   ],
   "source": [
    "X = 7\n",
    "m, N, n = [50, 500, 100]\n",
    "print(f'The probability of *X={X}* in the HG{N,m,n} Distribution is: ',  hypergeom.pmf(X, n = m, M = N, N = n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "id": "5S8stnBUpQdU",
    "outputId": "b87502dc-db2c-4a9d-c975-4c245dbea743"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1 = list(np.arange(0,X))\n",
    "x2 = X\n",
    "x3 = list(np.arange(X+1,22))\n",
    "plt.bar(x1, hypergeom.pmf(x1, n = m, M = N, N = n), color ='gray')\n",
    "plt.bar(x2, hypergeom.pmf(x2, n = m, M = N, N = n), color ='#DFFF00')\n",
    "plt.bar(x3, hypergeom.pmf(x3, n = m, M = N, N = n), color ='gray')\n",
    "plt.xlim(0,22)\n",
    "plt.xticks(np.arange(0,22), fontsize=12, ha='center')\n",
    "plt.title(f'$HG{N,m,n}$')\n",
    "prob = hypergeom.pmf(x2, n = m, M = N, N = n)\n",
    "plt.text(15, 0.02, f'$P({np.round(X, 3)}) = $ {np.round(prob, 2)}', fontsize=18);"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [
    "WJhmgDxsVHEO",
    "5z2nOmnTrKxu",
    "c1_c9ACB5Q_j",
    "eAUshqfZd-_d",
    "XMMnBa5iJUpD",
    "Bl35Ww-5HNtN",
    "dtrIR0AZhZla",
    "tDQwSzWJeoz2"
   ],
   "name": "Chapter 2: Special Discrete Random Variables.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}