{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Week 5-6: Continuous random variables\n",
    "\n",
    "\n",
    " #### [Back to main page](https://petrosyan.page/fall2020math3215)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Definition (cdf)**\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "Let $X$ be any random variable (does not have to be discrete). Define the cdf of $X$ as before\n",
    "\n",
    "$$F(x)=P(X\\leq x).$$\n",
    "\n",
    "</div>    \n",
    "  \n",
    "  \n",
    "**Definition (Continuous random variable)**\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "    \n",
    "A function $F:\\mathbb{R}\\to [0,1]$ is a cdf of some random variable,  if and only if\n",
    "\n",
    "1. $F$ is non-decreasing:\n",
    "$x\\leq y\\Rightarrow F(x)\\leq F(y)$\n",
    "\n",
    "2. $\\lim\\limits_{x\\to -\\infty}F(x)=0$\n",
    "\n",
    "3. $\\lim\\limits_{x\\to \\infty}F(x)=1$\n",
    "\n",
    "4. $F$ is  right continuous: for any $x\\in \\mathbb{R}$, $\\lim\\limits_{y\\to x^+}f(y)=f(x).$\n",
    "    \n",
    "</div>    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An example of a pdf is given by \n",
    "\n",
    "$$f(x)=\\frac{1}{\\pi}\\frac{\\sin^2x}{ x^2}, \\quad x\\in\\mathbb{R}.$$\n",
    "\n",
    "This is indeed a pdf, because it is non-negative and, as it can be checked,  \n",
    "\n",
    "$$\\int\\limits_\\mathbb{R}\\frac{\\sin^2x}{ x^2}=\\pi.$$\n",
    "\n",
    "Below we plot the pdf of this distribution.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "68b845473cba4b77abfe669e2dbc8c31",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.6, description='x', max=10.0, min=-10.0, readout_format=''), Output(…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from ipywidgets import interact, FloatSlider\n",
    "\n",
    "x=0.5\n",
    "def cdf_pdf(x):\n",
    "    xdata = np.delete(np.linspace(-10, 10, 1000), [0])\n",
    "    def pdf_func(x):\n",
    "        y = np.divide(np.sin(x)**2,x**2)/np.pi\n",
    "        return y\n",
    "\n",
    "\n",
    "    plt.plot(xdata, pdf_func(xdata))\n",
    "    xshade = xdata[xdata<=x]\n",
    "    plt.fill_between(xshade, pdf_func(xshade), alpha=0.3)\n",
    "    plt.scatter(x,0, s=30)\n",
    "    plt.rcParams['figure.figsize'] = (8, 4)\n",
    "    plt.axhline(y=0, color='k', linewidth=0.5)\n",
    "    plt.xlim(-11,11)\n",
    "    plt.ylim(-0.01,0.35)\n",
    "    plt.xticks([x],[\"x={}\".format(x)])\n",
    "    plt.yticks(np.arange(0,1,2))\n",
    "    plt.figtext(0.6,0.6, r\"$f(x)=\\frac{\\sin^2x}{ \\pi x^2}$\", ha=\"left\", va=\"top\",\n",
    "            backgroundcolor=(0, 0, 0, 0), fontsize=\"large\")\n",
    "    plt.box(on=None)\n",
    "    plt.show();\n",
    "\n",
    "# create interactive variables\n",
    "x = FloatSlider(min=-10.0, max=10.0, step=0.1, value=0.6, readout_format='')\n",
    "\n",
    "# display the interactive plot\n",
    "interact(cdf_pdf, x=x);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Logistic function\n",
    "\n",
    "$$F(X)=\\frac{e^x}{1+e^x}\\quad \\Rightarrow \\quad  f(x)=\\frac{e^x}{(1+e^x)^2}.$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9769f870b6c644d48ff36e7bd93a532d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.6, description='x', max=10.0, min=-10.0, readout_format=''), Output(…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from ipywidgets import interact, FloatSlider\n",
    "plt.rcParams['figure.figsize'] = (16, 5)\n",
    "\n",
    "\n",
    "def logistic_cdf_pdf(x):\n",
    "    xdata = np.linspace(-10, 10, 1000)\n",
    "    def cdf_func(xdata):\n",
    "        val = np.divide(np.exp(xdata), 1+np.exp(xdata))\n",
    "        return val\n",
    "    def pdf_func(xdata):\n",
    "        val = np.divide(np.exp(xdata), (1+np.exp(xdata)**2))\n",
    "        return val\n",
    "    \n",
    "    fig, [ax1, ax2] = plt.subplots(1, 2)\n",
    "    \n",
    "    ax1.plot(xdata, pdf_func(xdata))\n",
    "    xshade = xdata[xdata<=x]\n",
    "    ax1.fill_between(xshade, pdf_func(xshade), alpha=0.3)\n",
    "    ax1.scatter(x,0, s=30)\n",
    "    ax1.axhline(y=0, color='k', linewidth=0.5)\n",
    "    ax1.set_xlim(-10, 10)\n",
    "    ax1.set_ylim(-0.06,0.6)\n",
    "    ax1.set_xticks([x])\n",
    "    ax1.set_xticklabels([\"x={}\".format(x)])\n",
    "    ax1.set_title(\"pdf\")\n",
    "    \n",
    "    ax2.plot(xdata, cdf_func(xdata))\n",
    "    ax2.vlines(x, 0, cdf_func(x), linestyle=\"dashed\", alpha=0.4)\n",
    "    ax2.scatter(x,0, s=30)\n",
    "    ax2.axhline(y=0, color='k', linewidth=0.5)\n",
    "    ax2.set_xlim(-10, 10)\n",
    "    ax2.set_ylim(-0.1,1.1)\n",
    "    ax2.set_xticks([x])\n",
    "    ax2.set_xticklabels([\"x={}\".format(x)])\n",
    "    ax2.set_title(\"cdf\")\n",
    "    \n",
    "    plt.show();\n",
    "    \n",
    "# create interactive variables\n",
    "x = FloatSlider(min=-10, max=10, step=0.1, value=0.6, readout_format='')\n",
    "\n",
    "# display the interactive plot\n",
    "interact(logistic_cdf_pdf, x=x);    \n",
    "        \n",
    "        \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0502295ad18a45f086574cc5d9e508b4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.6, description='x', max=1.0, readout_format=''), IntSlider(value=0, …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from ipywidgets import interact, FloatSlider\n",
    "plt.rcParams['figure.figsize'] = (16, 5)\n",
    "\n",
    "a=0\n",
    "b=1\n",
    "\n",
    "def uniform_cdf_pdf(x, a=a, b=b):\n",
    "    xdata = np.linspace(a-1, b+1, 1000)\n",
    "    def cdf_func(xdata):\n",
    "        f0 = lambda y: (y-a)/(b-a)\n",
    "        val = np.piecewise(xdata, [xdata<a, (xdata>=a) & (xdata<=b), xdata>b], [0, f0, 1])\n",
    "        return val\n",
    "    def pdf_func(y):\n",
    "        val = np.piecewise(y, [y<a, (y>=a) & (y<=b), y>b], [0, 1, 0])\n",
    "        return val\n",
    "    \n",
    "    fig, [ax2, ax1] = plt.subplots(1, 2)\n",
    "    \n",
    "    ax1.plot(xdata, pdf_func(xdata))\n",
    "    xshade = xdata[xdata<=x]\n",
    "    ax1.fill_between(xshade, pdf_func(xshade), alpha=0.3)\n",
    "    ax1.scatter(x,0, s=30)\n",
    "    ax1.axhline(y=0, color='k', linewidth=0.5)\n",
    "    ax1.set_xlim(a-1, b+1)\n",
    "    ax1.set_ylim(-0.01,1)\n",
    "    ax1.set_xticks([a, x, b])\n",
    "    ax1.set_xticklabels([\"a={}\".format(a), \"x={}\".format(x), \"b={}\".format(b)])\n",
    "    ax1.set_frame_on(False)\n",
    "    ax1.set_title(\"pdf\")\n",
    "    \n",
    "    ax2.plot(xdata, cdf_func(xdata))\n",
    "    ax2.vlines(x, 0, cdf_func(x), linestyle=\"dashed\", alpha=0.4)\n",
    "    ax2.scatter(x,0, s=30)\n",
    "    ax2.axhline(y=0, color='k', linewidth=0.5)\n",
    "    ax2.set_xlim(a-1, b+1)\n",
    "    ax2.set_ylim(-0.01,1)\n",
    "    ax2.set_xticks([a, x, b])\n",
    "    ax2.set_xticklabels([\"a={}\".format(a), \"x={}\".format(x), \"b={}\".format(b)])\n",
    "    ax2.set_frame_on(False)\n",
    "    ax2.set_title(\"cdf\")\n",
    "    \n",
    "    plt.show();\n",
    "    \n",
    "# create interactive variables\n",
    "x = FloatSlider(min=-a, max=b, step=0.1, value=0.6, readout_format='')\n",
    "\n",
    "# display the interactive plot\n",
    "interact(uniform_cdf_pdf, x=x);    \n",
    "        \n",
    "        \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean of the uniform distribution is \n",
    "\n",
    "$$\\mu=\\frac{a+b}{2}.$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from ipywidgets import interact, FloatSlider\n",
    "plt.rcParams['figure.figsize'] = (12, 8)\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "lmbd = 0.8\n",
    "x=1\n",
    "\n",
    "xdata = np.linspace(-1, 10, 1000)\n",
    "def pdf_func(xdata):\n",
    "    f1 = lambda y: np.exp(-lmbd *(y + np.abs(y))/2)\n",
    "    val = np.piecewise(xdata, [xdata<0, xdata>=0], [0, f1])\n",
    "    return val\n",
    "\n",
    "\n",
    "plt.plot(xdata, pdf_func(xdata))\n",
    "xshade = xdata[xdata<=x]\n",
    "plt.fill_between(xshade, pdf_func(xshade), alpha=0.2)\n",
    "plt.xticks([x],[\"x={}\".format(x)])\n",
    "plt.axhline(y=0, color='k', linewidth=0.5)\n",
    "plt.box(on=None)\n",
    "plt.figtext(0.5,0.5, r\" $\\lambda=${}\".format(lmbd), ha=\"left\", va=\"top\",\n",
    "            backgroundcolor=(0.1, 0.1, 1, 0.15), fontsize=\"large\")\n",
    "plt.show();\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.special import gamma \n",
    "from ipywidgets import interact, FloatSlider\n",
    "plt.rcParams['figure.figsize'] = (12, 8)\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "\n",
    "Alpha = [1, 1.5,  2, 3]\n",
    "Theta = [3.5, 3.5, 3.5, 3.5 ]\n",
    "\n",
    "def pdf_func(xdata, alpha, theta):\n",
    "    f1 = lambda y: np.power(y, alpha-1)*np.exp(-y/2)/(np.power(theta,alpha)*gamma(alpha))\n",
    "    val = np.piecewise(xdata, [xdata<0, xdata>=0], [0, f1])\n",
    "    return val\n",
    "\n",
    "fix, ax = plt.subplots()\n",
    "\n",
    "def pplot_gamma(theta, alpha, ax):\n",
    "    xdata = np.linspace(-1, 20, 1000)\n",
    "    ax.plot(xdata, pdf_func(xdata, alpha, theta), label=r\"$\\theta=${}, $\\alpha=${}\".format(theta, alpha))\n",
    "    ax.axhline(y=0, color='k', linewidth=0.5)\n",
    "    ax.set_frame_on(False)\n",
    "\n",
    "\n",
    "for t,a in zip(Theta, Alpha):\n",
    "    pplot_gamma(t, a, ax)\n",
    "  \n",
    "ax.set_title(\"pdf of Gamma distribution\")\n",
    "plt.legend()  \n",
    "plt.show();\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.special import gamma \n",
    "from ipywidgets import interact, FloatSlider\n",
    "plt.rcParams['figure.figsize'] = (12, 8)\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "\n",
    "r_values = [2, 3, 4, 5, 10]\n",
    "\n",
    "def pdf_func(xdata, alpha, theta):\n",
    "    f1 = lambda y: np.power(y, alpha-1)*np.exp(-y/2)/(np.power(theta,alpha)*gamma(alpha))\n",
    "    val = np.piecewise(xdata, [xdata<0, xdata>=0], [0, f1])\n",
    "    return val\n",
    "\n",
    "fix, ax = plt.subplots()\n",
    "\n",
    "def pplot_chi(r):\n",
    "    alpha = r/2\n",
    "    xdata = np.linspace(-1, 30, 1000)\n",
    "    ax.plot(xdata, pdf_func(xdata, alpha, theta=2), label=\"r={}\".format(r))\n",
    "    ax.axhline(y=0, color='k', linewidth=0.5)\n",
    "    ax.set_frame_on(False)\n",
    "\n",
    "\n",
    "for r in r_values:\n",
    "    pplot_chi(r)\n",
    "  \n",
    "ax.set_title(r\"pdf of $\\chi^2$ distribution\")\n",
    "plt.legend()  \n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.special import gamma \n",
    "from ipywidgets import interact, FloatSlider\n",
    "plt.rcParams['figure.figsize'] = (12, 8)\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "\n",
    "Mu = [0,  -15, 10]\n",
    "Sigma = [1, 7, 5 ]\n",
    "\n",
    "def pdf_func(xdata, mu, sigma):\n",
    "    val = np.exp(-np.power(xdata-mu,2)/(2*sigma**2))/(sigma *np.sqrt(2*np.pi))\n",
    "    return val\n",
    "\n",
    "fix, ax = plt.subplots()\n",
    "\n",
    "def pplot_gamma(mu, sigma, ax):\n",
    "    xdata = np.linspace(-40, 40, 1000)\n",
    "    ax.plot(xdata, pdf_func(xdata, mu, sigma), label=r\"$\\mu=${},   $\\sigma=${}\".format(mu, sigma))\n",
    "    ax.axhline(y=0, color='k', linewidth=0.5)\n",
    "    ax.set_frame_on(False)\n",
    "\n",
    "\n",
    "for mu,sigma in zip(Mu, Sigma):\n",
    "    pplot_gamma(mu, sigma, ax)\n",
    "  \n",
    "ax.set_title(\"pdf of normal distribution\")\n",
    "plt.xticks(Mu)\n",
    "plt.legend()  \n",
    "plt.show();\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.special import gamma \n",
    "from ipywidgets import interact, FloatSlider\n",
    "plt.rcParams['figure.figsize'] = (12, 8)\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "\n",
    "mu=0\n",
    "sigma =1\n",
    "alpha = 0.05\n",
    "z  = 1.645\n",
    "\n",
    "def pdf_func(xdata, mu, sigma):\n",
    "    val = np.exp(-np.power(xdata-mu,2)/(2*sigma**2))/(sigma *np.sqrt(2*np.pi))\n",
    "    return val\n",
    "\n",
    "fix, ax = plt.subplots()\n",
    "\n",
    "def pplot_gamma(mu, sigma, ax, z):\n",
    "    xdata = np.linspace(-5, 5, 1000)\n",
    "    xshade = xdata[xdata-mu/sigma>=-z]\n",
    "    ax.fill_between(xshade, pdf_func(xshade, mu, sigma), alpha=0.3 )\n",
    "    #xshade = xdata[xdata-mu/sigma<=-z]\n",
    "    #ax.fill_between(xshade, pdf_func(xshade, mu, sigma), alpha=0.3, color=\"blue\")\n",
    "    ax.plot(xdata, pdf_func(xdata, mu, sigma), label=r\"$\\mu=${},   $\\sigma=${}\".format(mu, sigma))\n",
    "    ax.axhline(y=0, color='k', linewidth=0.5)\n",
    "\n",
    "\n",
    "pplot_gamma(mu, sigma, ax, z)\n",
    "  \n",
    "ax.set_title(\"pdf of standard normal distribution\")\n",
    "plt.xticks([-4,0,4])\n",
    "plt.legend()  \n",
    "plt.show();\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # nbi:hide_in\n",
    "\n",
    "\n",
    "##### These are for the homeworkproblems #####\n",
    "\n",
    "\n",
    "# import matplotlib.pyplot as plt\n",
    "# import numpy as np\n",
    "# from ipywidgets import interact, FloatSlider\n",
    "# plt.rcParams['figure.figsize'] = (12, 8)\n",
    "# import matplotlib as mpl\n",
    "# mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "# lmbd = 0.8\n",
    "# x=1\n",
    "\n",
    "# xdata = np.linspace(-1, 10, 1000)\n",
    "# def pdf_func(xdata):\n",
    "#     f1 = lambda y: np.exp(-lmbd *(y + np.abs(y))/2)\n",
    "#     val = np.piecewise(xdata, [xdata<0, xdata>=0], [0, f1])\n",
    "#     return val\n",
    "\n",
    "\n",
    "# plt.plot(xdata, pdf_func(xdata))\n",
    "# xshade = xdata[xdata<=x]\n",
    "# plt.fill_between(xshade, pdf_func(xshade), alpha=0.2)\n",
    "# plt.xticks([x],[\"x={}\".format(x)])\n",
    "# plt.axhline(y=0, color='k', linewidth=0.5)\n",
    "# plt.box(on=None)\n",
    "# plt.figtext(0.5,0.5, r\" $\\lambda=${}\".format(lmbd), ha=\"left\", va=\"top\",\n",
    "#             backgroundcolor=(0.1, 0.1, 1, 0.15), fontsize=\"large\")\n",
    "# plt.show();\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # nbi:hide_in\n",
    "# import matplotlib.pyplot as plt\n",
    "# import numpy as np\n",
    "# from ipywidgets import interact, FloatSlider\n",
    "# plt.rcParams['figure.figsize'] = (12, 8)\n",
    "# import matplotlib as mpl\n",
    "# mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "# lmbd = 0.8\n",
    "# x=1\n",
    "\n",
    "# xdata = np.linspace(-1, 3, 1000)\n",
    "# def pdf_func(xdata):\n",
    "#     f1 = lambda y: np.power(y,4)/16\n",
    "#     val = np.piecewise(xdata, [xdata<0, (xdata>=0) & (xdata<=2), xdata>=2], [0, f1, 1])\n",
    "#     return val\n",
    "\n",
    "\n",
    "# plt.plot(xdata, pdf_func(xdata))\n",
    "# xshade = xdata[xdata<=x]\n",
    "# plt.axhline(y=0, color='k', linewidth=0.5)\n",
    "# plt.title(\"cdf\")\n",
    "# plt.show();\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # nbi:hide_in\n",
    "# import matplotlib.pyplot as plt\n",
    "# import numpy as np\n",
    "# from ipywidgets import interact, FloatSlider\n",
    "# plt.rcParams['figure.figsize'] = (12, 8)\n",
    "# import matplotlib as mpl\n",
    "# mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "# lmbd = 0.8\n",
    "# x=1\n",
    "\n",
    "# xdata = np.linspace(-1, 3, 1000)\n",
    "# def pdf_func(xdata):\n",
    "#     f1 = lambda y: np.power(y,3)/4\n",
    "#     val = np.piecewise(xdata, [xdata<0, (xdata>=0) & (xdata<=2), xdata>=2], [0, f1, 0])\n",
    "#     return val\n",
    "\n",
    "\n",
    "# plt.plot(xdata, pdf_func(xdata))\n",
    "# xshade = xdata[xdata<=x]\n",
    "# plt.axhline(y=0, color='k', linewidth=0.5)\n",
    "# plt.title(\"pdf\")\n",
    "# plt.show();\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # nbi:hide_in\n",
    "# import matplotlib.pyplot as plt\n",
    "# import numpy as np\n",
    "# from ipywidgets import interact, FloatSlider\n",
    "# plt.rcParams['figure.figsize'] = (12, 8)\n",
    "# import matplotlib as mpl\n",
    "# mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "\n",
    "\n",
    "\n",
    "# xdata = np.linspace(-3,3, 1000)\n",
    "# def pdf_func(xdata):\n",
    "#     f1 = lambda y: np.power(y,3)/16+0.5\n",
    "#     val = np.piecewise(xdata, [xdata<-2, (xdata>=-2) & (xdata<=2), xdata>=2], [0, f1, 1])\n",
    "#     return val\n",
    "\n",
    "\n",
    "# plt.plot(xdata, pdf_func(xdata))\n",
    "# xshade = xdata[xdata<=x]\n",
    "# plt.axhline(y=0, color='k', linewidth=0.5)\n",
    "# plt.title(\"cdf\")\n",
    "# plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # nbi:hide_in\n",
    "# import matplotlib.pyplot as plt\n",
    "# import numpy as np\n",
    "# from ipywidgets import interact, FloatSlider\n",
    "# plt.rcParams['figure.figsize'] = (12, 8)\n",
    "# import matplotlib as mpl\n",
    "# mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "# lmbd = 0.8\n",
    "# x=1\n",
    "\n",
    "# xdata = np.linspace(-3, 3, 1000)\n",
    "# def pdf_func(xdata):\n",
    "#     f1 = lambda y: np.power(y,2)/16\n",
    "#     val = np.piecewise(xdata, [xdata<-2, (xdata>=-2) & (xdata<=2), xdata>=2], [0, f1, 0])\n",
    "#     return val\n",
    "\n",
    "\n",
    "# plt.plot(xdata, pdf_func(xdata))\n",
    "# xshade = xdata[xdata<=x]\n",
    "# plt.axhline(y=0, color='k', linewidth=0.5)\n",
    "# plt.title(\"pdf\")\n",
    "# plt.show();\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # nbi:hide_in\n",
    "# import matplotlib.pyplot as plt\n",
    "# import numpy as np\n",
    "# from ipywidgets import interact, FloatSlider\n",
    "# plt.rcParams['figure.figsize'] = (12, 8)\n",
    "# import matplotlib as mpl\n",
    "# mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "# lmbd = 0.8\n",
    "# x=1\n",
    "\n",
    "# xdata = np.linspace(-1, 2, 1001)\n",
    "# def pdf_func(xdata):\n",
    "#     f1 = lambda y: np.power(y,0.5)\n",
    "#     val = np.piecewise(xdata, [xdata<0, (xdata>=0) & (xdata<=1), xdata>=1], [0, f1, 1])\n",
    "#     return val\n",
    "\n",
    "\n",
    "# plt.plot(xdata, pdf_func(xdata))\n",
    "# xshade = xdata[xdata<=x]\n",
    "# plt.axhline(y=0, color='k', linewidth=0.5)\n",
    "# plt.title(\"cdf\")\n",
    "# plt.show();\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # nbi:hide_in\n",
    "# import matplotlib.pyplot as plt\n",
    "# import numpy as np\n",
    "# from ipywidgets import interact, FloatSlider\n",
    "# plt.rcParams['figure.figsize'] = (12, 8)\n",
    "# import matplotlib as mpl\n",
    "# mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "# lmbd = 0.8\n",
    "# x=1\n",
    "\n",
    "# xdata = np.linspace(-1, 2, 1001)\n",
    "# def pdf_func(xdata):\n",
    "#     f1 = lambda y: np.reciprocal(np.power(y,0.5))/2\n",
    "#     val = np.piecewise(xdata, [xdata<0, (xdata>=0) & (xdata<=1), xdata>=1], [0, f1, 0])\n",
    "#     return val\n",
    "\n",
    "\n",
    "# plt.plot(xdata, pdf_func(xdata))\n",
    "# xshade = xdata[xdata<=x]\n",
    "# plt.axhline(y=0, color='k', linewidth=0.5)\n",
    "# plt.title(\"pdf\")\n",
    "# plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # nbi:hide_in\n",
    "# import matplotlib.pyplot as plt\n",
    "# import numpy as np\n",
    "# from ipywidgets import interact, FloatSlider\n",
    "# plt.rcParams['figure.figsize'] = (12, 8)\n",
    "# import matplotlib as mpl\n",
    "# mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "# lmbd = 0.8\n",
    "# x=1\n",
    "\n",
    "# xdata = np.linspace(-1, 3, 1001)\n",
    "# def cdf_func(xdata):\n",
    "#     f1 = lambda y: np.power(y,2)/4\n",
    "#     f2 = lambda y: (y+1)/4\n",
    "#     val = np.piecewise(xdata, [xdata<0, (xdata>=0) & (xdata<1),(xdata>=1) & (xdata<2), xdata>=2], [0, f1, f2, 1])\n",
    "#     return val\n",
    "\n",
    "\n",
    "# plt.plot(xdata, cdf_func(xdata))\n",
    "# xshade = xdata[xdata<=x]\n",
    "# plt.axhline(y=0, color='k', linewidth=0.5)\n",
    "# plt.title(\"cdf\")\n",
    "# plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YRsgiACKJMAIgIC/TNAD6CWEEQEAGC1gB9BPCCICAGBkB0F8IIwACYs0IgP5CGAEQkC+MOBzsFAsgsggjAALyDYwwRQMg0ggjAALyjYyweBVApBFGAATkW8DKFA2ASCOMAAjI25lGnIQRABFGGAEQENM0APoLYQRAQF4WsALoJyGFkVWrViknJ0dJSUnKz8/X1q1bL3p+W1ubli1bptGjR8vlcunyyy/X2rVrQyoYQP+48NZeAIik+GAvqKio0JIlS7Rq1SpNmzZNzz//vObOnatdu3Zp1KhRAa+ZN2+ejh07pjVr1uiKK65QQ0ODOjo6+lw8gMjxtYOPY54GQIQFHUZWrFihBQsWaOHChZKklStX6q233lJ5ebnKysq6nf+nP/1Jmzdv1v79+zV06FBJ0pgxY/pWNYCIY5oGQH8Japqmvb1d1dXVKiws7HK8sLBQ27ZtC3jN+vXrVVBQoH/913/VpZdeqnHjxunBBx/U6dOne3ydtrY2ud3uLg8A/YsFrAD6S1AjI42NjfJ4PMrMzOxyPDMzU/X19QGv2b9/v9577z0lJSXpzTffVGNjo37+85/r+PHjPa4bKSsr0xNPPBFMaQDCzOs991/6jACItJAWsH77w8kwjB4/sLxerxwOh15++WVde+21uvnmm7VixQqtW7eux9GR0tJSNTc3+x+HDh0KpUwAfcDICID+EtTISHp6upxOZ7dRkIaGhm6jJT4jRozQpZdeqtTUVP+x3NxcGYahw4cPa+zYsd2ucblccrlcwZQGIMzYmwZAfwlqZCQxMVH5+fmqqqrqcryqqkpTp04NeM20adN09OhRnTx50n9s7969iouL08iRI0MoGUB/OD8yQhgBEFlBT9OUlJTohRde0Nq1a7V7924tXbpUtbW1Ki4ulnRuimX+/Pn+8++8806lpaXp3nvv1a5du7RlyxY99NBD+ulPf6rk5OTwvRMAYUWfEQD9Jehbe4uKitTU1KTly5errq5OeXl5qqys1OjRoyVJdXV1qq2t9Z8/aNAgVVVV6YEHHlBBQYHS0tI0b948Pfnkk+F7FwDCjlt7AfQXh+HrbBTF3G63UlNT1dzcrJSUFLPLAWLCjq+O6/88t11j0gZo00OzzC4HgAX19uc3e9MACMg/MsLtNAAijDACICAWsALoL4QRAAHRZwRAfyGMAAiIPiMA+gthBEBA52/tJYwAiCzCCICAPF6maQD0D8IIgICYpgHQXwgjAAJiASuA/kIYARCQr88Ia0YARBphBEBAjIwA6C+EEQABGTQ9A9BPCCMAAmKjPAD9hTACIKDzfUZMLgSA7RFGAATkGxlxsmgEQIQRRgAExJoRAP2FMAIgIKZpAPQXwgiAgLzec/9lZARApBFGAAREnxEA/YUwAiAg9qYB0F8IIwACOr9mhDACILIIIwACOt/0zNw6ANgfYQRAQF5u7QXQTwgjAALy9xnhUwJAhPExAyAgj5c1IwD6B2EEQEBslAegv8SbXQBgR5Wf1OnDr46bXUaffHbULYkFrAAijzAChFnlJ3X6+csfmV1G2KQkJZhdAgCbI4wAYfZ69WFJ0vdGpGjW+GEmV9M3rnin5hVkm10GAJsjjABhdLrdo/e+bJQkPTVvgnJHpJhcEQBEPxawAmG0bV+j2jq8unRIssYPH2x2OQBgCYQRIIw27GmQJM0en8EtsQDQS4QRIEwMw9DG3Z1hJDfD5GoAwDoII0CYfHbUrXr3GSUnODXlsjSzywEAyyCMAGGysXOKZvrYdCUlOE2uBgCsgzAChIlvvcic8UzRAEAwCCNAGDS0nNHHh76RdG7xKgCg9wgjQBhs2vO1JOmqkanKSEkyuRoAsBbCCBAGG/Yck8SoCACEgjAC9NGZsx5t/eJc19UbcjNNrgYArIcwAvTRnw8c16l2jzJTXPp+Fu3fASBYhBGgjzbsPj9FQ9dVAAgeYQToA8MwtGG375ZepmgAIBSEEaAP9h47qSPfnJYrPk7Trkg3uxwAsCTCCNAH73RO0Uy7Il3JiXRdBYBQEEaAPth4wS69AIDQEEaAEB1vbddHtSckEUYAoC8II0CI3t3TIMOQvjciRVlDks0uBwAsizAChMg3RTMnl1ERAOgLwggQgvYOr7bsPbcfDVM0ANA3hBEgBB9+dVwtbR1KH5SoCSOHmF0OAFgaYQQIga/R2awrMxQXR9dVAOgLwggQJMMw/Lv0sl4EAPqOMAIEad/XrTrYdEqJzjhNHzvM7HIAwPIII0CQNnaOiky+bKgGueJNrgYArI8wAgTp/MZ4TNEAQDgQRoAgNJ86qx0Hz3VdnZPLLr0AEA4hhZFVq1YpJydHSUlJys/P19atW3t13fvvv6/4+HhNnDgxlJcFTLdpb4M8XkPjMgcpe+gAs8sBAFsIOoxUVFRoyZIlWrZsmWpqajRjxgzNnTtXtbW1F72uublZ8+fP15w5c0IuFjDb+Y3xGBUBgHAJOoysWLFCCxYs0MKFC5Wbm6uVK1cqOztb5eXlF73uvvvu05133qkpU6aEXCxgpg6PV5s+P9d19QZu6QWAsAkqjLS3t6u6ulqFhYVdjhcWFmrbtm09Xvfiiy9q3759+uUvf9mr12lra5Pb7e7yAMxWffCEmk+f1ZABCbp61CVmlwMAthFUGGlsbJTH41FmZtch6szMTNXX1we85osvvtAjjzyil19+WfHxvbsNsqysTKmpqf5HdnZ2MGUCEeGbopl1ZYacdF0FgLAJaQGrw9H1g9gwjG7HJMnj8ejOO+/UE088oXHjxvX6+UtLS9Xc3Ox/HDp0KJQygbB6ZzddVwEgEoLq2JSeni6n09ltFKShoaHbaIkktbS0aMeOHaqpqdH9998vSfJ6vTIMQ/Hx8Xr77bc1e/bsbte5XC65XK5gSgMi6qvGVu37ulXxcQ7NoOsqAIRVUCMjiYmJys/PV1VVVZfjVVVVmjp1arfzU1JS9Mknn2jnzp3+R3Fxsa688krt3LlTkydP7lv1QD/xTdFcM2aoUpMTTK4GAOwl6F7WJSUluuuuu1RQUKApU6Zo9erVqq2tVXFxsaRzUyxHjhzRSy+9pLi4OOXl5XW5PiMjQ0lJSd2OA9GMjfEAIHKCDiNFRUVqamrS8uXLVVdXp7y8PFVWVmr06NGSpLq6uu/sOQJYScuZs/rz/uOS6LoKAJHgMAzDMLuI7+J2u5Wamqrm5malpKSYXQ5izH//tU6LXvlIl6UP1MYHZ5pdDgBYRm9/frM3DfAdmKIBgMgijAAX4fEa/q6rtIAHgMggjAAXsfPQCR1vbdfgpHgVjKHrKgBEAmEEuIgNu8/d0jvzygwlOPnrAgCRwKcrcBG+/iJzxrNeBAAihTAC9ODwiVPaU9+iOId0/Ti6rgJApBBGgB74RkUKRg/VJQMTTa4GAOyLMAL0wLdeZDa39AJARBFGgABa2zq0fV+TJNaLAECkEUaAAN77slHtHq9GDR2gKzIGmV0OANgaYQQIYKNvimZ8hhwOh8nVAIC9EUaAb/F6DW3w3dLLehEAiDjCCPAtnxxpVuPJNg1MdGpyTprZ5QCA7RFGgG/xjYpcN26YEuP5KwIAkcYnLfAtG3b7dullYzwA6A+EEeAC9c1n9NlRtxwOaeaVdF0FgP5AGAEu4Ou6OjF7iNIHuUyuBgBiA2EEuIBviuYGpmgAoN8QRoBOp9s9eu/LRknn+osAAPoHYQTotH1/o9o6vMpKTdL44YPNLgcAYgZhBOj0zm5fo7NMuq4CQD8ijACSDMM43wKerqsA0K8II4CkXXVu1bvPKDnBqSmX0XUVAPoTYQSQtKFzVGT62HQlJThNrgYAYgthBND5FvBzuIsGAPodYQQxr6HljD4+9I0kbukFADMQRhDzNu35WpJ01chUZaQkmVwNAMQewghi3oY957quMioCAOYgjCCmnTnr0dYvznVdnTOeFvAAYAbCCGLanw8c16l2jzJTXMq7NMXscgAgJhFGENM27j4/RUPXVQAwB2EEMcswDH8L+NlM0QCAaQgjiFl7j53UkW9OyxUfp+lXpJtdDgDELMIIYpbvLpqpl6cpOZGuqwBgFsIIYtYG/8Z4TNEAgJkII4hJx1vb9VHtCUm0gAcAsxFGEJM2fd4gw5ByR6Qoa0iy2eUAQEwjjCAm+aZoGBUBAPMRRhBz2ju82rL33H40c3IJIwBgNsIIYs6Or46rpa1DaQMTNWHkELPLAYCYRxhBzPE1Ops1PkNxcXRdBQCzEUYQUwzD8PcXuYEpGgCICoQRxJT9ja062HRKCU6Hpo8dZnY5AAARRhBjNnRujPeDy9I0yBVvcjUAAIkwghjDLb0AEH0II4gZzafOasfBc11X2aUXAKIHYQQxY9PeBnm8hsZmDNKotAFmlwMA6EQYQczYuKdzioaN8QAgqhBGEBM6PF5t+pyuqwAQjQgjiAnVB0+o+fRZDRmQoEmjLjG7HADABQgjiAm+KZpZV2bISddVAIgqhBHEhHc6+4vM5pZeAIg6hBHY3leNrdr3davi4xy6bhxdVwEg2hBGYHu+KZprxgxVanKCydUAAL6NMALb822Mx100ABCdCCOwtZYzZ/Xn/ccl0V8EAKJVSGFk1apVysnJUVJSkvLz87V169Yez33jjTf0wx/+UMOGDVNKSoqmTJmit956K+SCgWBs/aJRHV5Dl6UPVE76QLPLAQAEEHQYqaio0JIlS7Rs2TLV1NRoxowZmjt3rmprawOev2XLFv3whz9UZWWlqqurNWvWLN16662qqanpc/HAd+EuGgCIfg7DMIxgLpg8ebImTZqk8vJy/7Hc3FzddtttKisr69VzfP/731dRUZEee+yxXp3vdruVmpqq5uZmpaSkBFMuYpjHa+ia//uOjre269Wf/UBTLk8zuyQAiCm9/fkd1MhIe3u7qqurVVhY2OV4YWGhtm3b1qvn8Hq9amlp0dChQ3s8p62tTW63u8sDCNbOQ9/oeGu7BifFq2AMXVcBIFoFFUYaGxvl8XiUmdl1IWBmZqbq6+t79RxPPfWUWltbNW/evB7PKSsrU2pqqv+RnZ0dTJmAJGlD5xTN9eOGKcHJWm0AiFYhfUI7HF3baRuG0e1YIK+++qoef/xxVVRUKCOj5zn80tJSNTc3+x+HDh0KpUzEOF9/kRu4iwYAolp8MCenp6fL6XR2GwVpaGjoNlrybRUVFVqwYIFee+013XDDDRc91+VyyeVyBVMa0MXhE6e0p75FcY5zIyMAgOgV1MhIYmKi8vPzVVVV1eV4VVWVpk6d2uN1r776qu655x698soruuWWW0KrFAiCb1Qkf/QlumRgosnVAAAuJqiREUkqKSnRXXfdpYKCAk2ZMkWrV69WbW2tiouLJZ2bYjly5IheeuklSeeCyPz58/Uf//Ef+sEPfuAfVUlOTlZqamoY3wpw3obd58IIjc4AIPoFHUaKiorU1NSk5cuXq66uTnl5eaqsrNTo0aMlSXV1dV16jjz//PPq6OjQokWLtGjRIv/xu+++W+vWrev7OwC+pbWtQ9v3NUmS5tBfBACiXtB9RsxAnxEE463P6nXf/6tW9tBkbXloVq8WVwMAwi8ifUYAK9jom6IZn0kQAQALIIzAVrxeQxs/960XYYoGAKyAMAJb+eRIs75uadPARKeuzem5yy8AIHoQRmArGzpv6b1u3DC54p0mVwMA6A3CCGxl4x526QUAqyGMwDbqm8/o0yNuORzSLMIIAFgGYQS24eu6OjF7iNIHsZ0AAFgFYQS24dull0ZnAGAthBHYwul2j977slGSNHs8LeABwEoII7CF7fsb1dbhVVZqknJHDDa7HABAEAgjsIV3Oruuzs7NoOsqAFgMYQSWZxhGlxbwAABrIYzA8nbVuVXvPqPkBKemXJ5mdjkAgCARRmB5GzpHRaZdka6kBLquAoDVEEZgeb4W8GyMBwDWRBiBpX3d0qaPD30jiRbwAGBVhBFY2rudoyL/69JUZaYkmVwNACAUhBFY2obOjfGYogEA6yKMwLLaOjza+sW5rqvc0gsA1kUYgWV9sP+4TrV7lDHYpe9npZhdDgAgRIQRWNbG3eenaOLi6LoKAFZFGIElGYbhv6WXjfEAwNoII7CkvcdO6vCJ00qMj9O0K+i6Cgzm5K0AAAstSURBVABWRhiBJfnuopl2eZoGJMabXA0AoC8II7Ckjf5depmiAQCrI4zAco63tuuj2hOS6LoKAHZAGIHlbPq8QV5Dyh2RokuHJJtdDgCgjwgjsBz/xniMigCALRBGYCntHV5t+fxrSdJsWsADgC0QRmApO746rpa2DqUNTNTEkUPMLgcAEAaEEViKb4pm1ni6rgKAXRBGYBmGYWiDrwU860UAwDYII7CM/Y2t+qrplBKcDs0YN8zscgAAYUIYgWX4RkV+cFmaBrnougoAdkEYgWVs8HVdZYoGAGyFMAJLaD51VjsOnuu6OoddegHAVggjsIRNexvk8RoamzFIo9IGmF0OACCMCCOwhI17fBvjMUUDAHZDGEHU6/B4tamz6+oN7NILALZDGEHUqz54Qs2nz2rIgARdnU3XVQCwG8IIop5vimbmuGGKd/JHFgDshk92RD3/Lr1M0QCALRFGENUONrXqy4aTcsY5dB1dVwHAlggjiGq+RmfXjLlEqckJJlcDAIgEwgiimm+9CHfRAIB9EUYQtVrOnNWfDzRJogU8ANgZYQRRa+sXjTrrMZSTPlCXDRtkdjkAgAghjCBq+daLzGFUBABsjTCCqOTxGnr3c1rAA0AsIIwgKu089I2Ot7ZrcFK8rhkz1OxyAAARRBhBVNq455gk6fpxw5RA11UAsDU+5RGV/OtFmKIBANsjjCDqHD5xSnvqWxTnkGaOI4wAgN0RRhB13u1sdJY/+hJdMjDR5GoAAJFGGEHUeadzimb2eLquAkAsIIwgqrS2dWj7vnNdV29gvQgAxATCCKLK+182qt3jVfbQZF2RQddVAIgFIYWRVatWKScnR0lJScrPz9fWrVsvev7mzZuVn5+vpKQkXXbZZXruuedCKhb2d77raqYcDofJ1QAA+kPQYaSiokJLlizRsmXLVFNToxkzZmju3Lmqra0NeP6BAwd08803a8aMGaqpqdGjjz6qxYsX6/XXX+9z8bAXr9fQxs+5pRcAYo3DMAwjmAsmT56sSZMmqby83H8sNzdXt912m8rKyrqd//DDD2v9+vXavXu3/1hxcbE+/vhjbd++PeBrtLW1qa2tzf+12+1Wdna2mpublZKSEky5F/V69WF9erQ5bM+Hvtl56BvV1H6jQa54Vf/iBrninWaXBADoA7fbrdTU1O/8+R0fzJO2t7erurpajzzySJfjhYWF2rZtW8Brtm/frsLCwi7HbrzxRq1Zs0Znz55VQkJCt2vKysr0xBNPdDteVFQU8PxQfXqkWfXuM2F7PoRHwpBk3VHzrNllAAD66OzZs706L6gw0tjYKI/Ho8zMrrdcZmZmqr6+PuA19fX1Ac/v6OhQY2OjRowY0e2a0tJSlZSU+L/2jYxUVFSEdWTkjx8f1Z56d9ieD32XnODUTyaPpr8IANiAb2TkuwQVRny+vbDQMIyLLjYMdH6g4z4ul0sulyuU0oJy64Qs3TohK+KvAwAAehbUAtb09HQ5nc5uoyANDQ3dRj98hg8fHvD8+Ph4paWlBVkuAACwm6DCSGJiovLz81VVVdXleFVVlaZOnRrwmilTpnQ7/+2331ZBQUFY138AAABrCvrW3pKSEr3wwgtau3atdu/eraVLl6q2tlbFxcWSzq33mD9/vv/84uJiHTx4UCUlJdq9e7fWrl2rNWvW6MEHHwzfuwAAAJYV9JqRoqIiNTU1afny5aqrq1NeXp4qKys1evRoSVJdXV2XniM5OTmqrKzU0qVL9eyzzyorK0u/+c1vdPvtt4fvXQAAAMsKus+IGXp7nzIAAIgevf35zd40AADAVIQRAABgKsIIAAAwFWEEAACYijACAABMRRgBAACmIowAAABTEUYAAICpQtq1t7/5+rK53W6TKwEAAL3l+7n9Xf1VLRFGWlpaJEnZ2dkmVwIAAILV0tKi1NTUHv+/JdrBe71eHT16VIMHD5bD4Qjb87rdbmVnZ+vQoUO0mY8SfE+iC9+P6ML3I7rw/fhuhmGopaVFWVlZiovreWWIJUZG4uLiNHLkyIg9f0pKCn+Qogzfk+jC9yO68P2ILnw/Lu5iIyI+LGAFAACmIowAAABTOR9//PHHzS7CTE6nUzNnzlR8vCVmrGIC35PowvcjuvD9iC58P8LDEgtYAQCAfTFNAwAATEUYAQAApiKMAAAAUxFGAACAqQgjAADAVISRTl999ZUWLFignJwcJScn6/LLL9cvf/lLtbe3m11azFi1apVycnKUlJSk/Px8bd261eySYlJZWZmuueYaDR48WBkZGbrtttv0+eefm10WOpWVlcnhcGjJkiVmlxLTjhw5or/7u79TWlqaBgwYoIkTJ6q6utrssiyLMNJpz5498nq9ev755/XZZ5/p3//93/Xcc8/p0UcfNbu0mFBRUaElS5Zo2bJlqqmp0YwZMzR37lzV1taaXVrM2bx5sxYtWqQPPvhAVVVV6ujoUGFhoVpbW80uLeZ9+OGHWr16ta666iqzS4lpJ06c0LRp05SQkKD/+Z//0a5du/TUU09pyJAhZpdmWfQZuYh/+7d/U3l5ufbv3292KbY3efJkTZo0SeXl5f5jubm5uu2221RWVmZiZfj666+VkZGhzZs367rrrjO7nJh18uRJTZo0SatWrdKTTz6piRMnauXKlWaXFZMeeeQRvf/++4zehhEjIxfR3NysoUOHml2G7bW3t6u6ulqFhYVdjhcWFmrbtm0mVQWf5uZmSeLvgskWLVqkW265RTfccIPZpcS89evXq6CgQHfccYcyMjJ09dVX67e//a3ZZVkaYaQH+/bt09NPP63i4mKzS7G9xsZGeTweZWZmdjmemZmp+vp6k6qCdG7775KSEk2fPl15eXlmlxOzfve73+mjjz5ilDBK7N+/X+Xl5Ro7dqzeeustFRcXa/HixXrppZfMLs2ybB9GHn/8cTkcjos+duzY0eWao0eP6qabbtIdd9yhhQsXmlR57HE4HF2+Ngyj2zH0r/vvv19//etf9eqrr5pdSsw6dOiQ/uEf/kH/+Z//qaSkJLPLgSSv16tJkybpV7/6la6++mrdd999+tnPftZlmhnBsf3OPvfff79+/OMfX/ScMWPG+H999OhRzZo1S1OmTNHq1asjXB0kKT09XU6ns9soSENDQ7fREvSfBx54QOvXr9eWLVs0cuRIs8uJWdXV1WpoaFB+fr7/mMfj0ZYtW/TMM8+ora1NTqfTxApjz4gRI/S9732vy7Hc3Fy9/vrrJlVkfbYPI+np6UpPT+/VuUeOHNGsWbOUn5+vF198UXFxth84igqJiYnKz89XVVWVfvSjH/mPV1VV6W/+5m9MrCw2GYahBx54QG+++aY2bdqknJwcs0uKaXPmzNEnn3zS5di9996r8ePH6+GHHyaImGDatGndbnffu3evRo8ebVJF1mf7MNJbR48e1cyZMzVq1Cj9+te/1tdff+3/f8OHDzexsthQUlKiu+66SwUFBf5RqdraWtbsmGDRokV65ZVX9F//9V8aPHiwf8QqNTVVycnJJlcXewYPHtxtvc7AgQOVlpbGOh6TLF26VFOnTtWvfvUrzZs3T3/5y1+0evVqRtP7gDDS6e2339aXX36pL7/8stuQNHc/R15RUZGampq0fPly1dXVKS8vT5WVlfxLwwS+ee+ZM2d2Of7iiy/qnnvu6f+CgChzzTXX6M0331RpaamWL1+unJwcrVy5Uj/5yU/MLs2y6DMCAABMxaIIAABgKsIIAAAwFWEEAACYijACAABMRRgBAACmIowAAABTEUYAAICpCCMAAMBUhBEAAGAqwggAADAVYQQAAJjq/wMSkJTQgdxT0wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from ipywidgets import interact, FloatSlider\n",
    "plt.rcParams['figure.figsize'] = (12, 8)\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "lmbd = 0.8\n",
    "x=1\n",
    "\n",
    "xdata = np.linspace(-2, 7, 1001)\n",
    "def cdf_func1(xdata):\n",
    "    f = lambda y: y\n",
    "    val = np.piecewise(xdata, [xdata<0, (xdata>=0) & (xdata<1), xdata>=1], [0, f, 1])\n",
    "    return val\n",
    "\n",
    "def cdf_func2(xdata):\n",
    "    val = np.piecewise(xdata, [xdata<2, (xdata>=2) & (xdata<4),(xdata>=4) & (xdata<6), xdata>=6], [0, 1/3, 2/3, 1])\n",
    "    return val\n",
    "\n",
    "plt.plot(xdata, cdf_func1(xdata)/2+cdf_func2(xdata)/2)\n",
    "xshade = xdata[xdata<=x]\n",
    "plt.axhline(y=0, color='k', linewidth=0.5)\n",
    "plt.title(\"cdf\")\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from ipywidgets import interact, FloatSlider\n",
    "plt.rcParams['figure.figsize'] = (12, 8)\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "lmbd = 0.8\n",
    "x=1\n",
    "\n",
    "xdata = np.linspace(-5, 5, 1001)\n",
    "def cdf_func1(xdata):\n",
    "    f = lambda y: np.exp(y)/(1+np.exp(y))\n",
    "    return f(xdata)\n",
    "\n",
    "def cdf_func2(xdata):\n",
    "    val = np.piecewise(xdata, [xdata<0, xdata>=0], [0, 1])\n",
    "    return val\n",
    "\n",
    "plt.plot(xdata, cdf_func1(xdata)/2+cdf_func2(xdata)/2)\n",
    "xshade = xdata[xdata<=x]\n",
    "plt.axhline(y=0, color='k', linewidth=0.5)\n",
    "plt.title(\"cdf of mixture\")\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from ipywidgets import interact, FloatSlider\n",
    "plt.rcParams['figure.figsize'] = (12, 8)\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "lmbd = 0.8\n",
    "x=1\n",
    "\n",
    "xdata = np.linspace(-5, 5, 1001)\n",
    "def cdf_func1(xdata):\n",
    "    f = lambda y: np.exp(y)/(1+np.exp(y))\n",
    "    return f(xdata)\n",
    "\n",
    "def cdf_func2(xdata):\n",
    "    val = np.piecewise(xdata, [xdata<0, xdata>=0], [0, 1])\n",
    "    return val\n",
    "\n",
    "plt.plot(xdata, cdf_func1(xdata))\n",
    "xshade = xdata[xdata<=x]\n",
    "plt.axhline(y=0, color='k', linewidth=0.5)\n",
    "plt.title(\"cdf of continuous\")\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from ipywidgets import interact, FloatSlider\n",
    "plt.rcParams['figure.figsize'] = (12, 8)\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "lmbd = 0.8\n",
    "x=1\n",
    "\n",
    "xdata = np.linspace(-5, 5, 1001)\n",
    "def cdf_func1(xdata):\n",
    "    f = lambda y: np.exp(y)/(1+np.exp(y))\n",
    "    return f(xdata)\n",
    "\n",
    "def cdf_func2(xdata):\n",
    "    val = np.piecewise(xdata, [xdata<0, xdata>=0], [0, 1])\n",
    "    return val\n",
    "\n",
    "plt.plot(xdata,  cdf_func2(xdata)/2)\n",
    "xshade = xdata[xdata<=x]\n",
    "plt.axhline(y=0, color='k', linewidth=0.5)\n",
    "plt.title(\"cdf of discrete\")\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "# nbi:hide_in\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams[\"figure.figsize\"] = (10, 5)\n",
    "\n",
    "N=1000\n",
    "num = 1000\n",
    "a=2\n",
    "b=4\n",
    "intsize = 50\n",
    "plot_width = 2\n",
    "\n",
    "data =np.random.rand(N, num)*(b-a)+a\n",
    "length=(b-a)/(intsize-1)\n",
    "mu = (b+a)/2\n",
    "\n",
    "def pdf_func(xdata, mu, sigma):\n",
    "    val = np.exp(-np.power(xdata-mu,2)/(2*sigma**2))/(sigma *np.sqrt(2*np.pi))\n",
    "    return val\n",
    "\n",
    "def epmf(x, inter):\n",
    "    epmf_values = np.zeros(intsize-1)\n",
    "    for i in range(intsize-1): \n",
    "        length = inter[i+1]-inter[i]\n",
    "        epmf_values[i] = np.sum((inter[i]<=x) & (x<inter[i+1]))/(x.size*length)\n",
    "    return epmf_values \n",
    "\n",
    "def mean_hist(n):\n",
    "    sigma = np.sqrt((b-a)**2/12)/np.sqrt(n)\n",
    "    xvalues = np.linspace(a,b, 1000)\n",
    "    plt.plot(xvalues, pdf_func(xvalues, mu, sigma), linewidth=2, color=\"red\")\n",
    "    x = np.sum(data[0:n,:], axis=0)/n\n",
    "    inter = np.linspace(a,b,intsize)\n",
    "    epmf_values = epmf(x, inter)\n",
    "    plt.bar(inter[:intsize-1], epmf_values, width=length, \n",
    "            color='#039be5', edgecolor='black', linewidth=1, \n",
    "            align=\"edge\", label=\"True histogran\")\n",
    "    plt.figtext(0.8,0.8, \"n = {}\".format(n), ha=\"left\", va=\"top\",\n",
    "        backgroundcolor=(0.1, 0.1, 1, 0.15), fontsize=\"large\")\n",
    "    plt.show();\n",
    "\n",
    "def mean_hist_std(n):\n",
    "    sigma = np.sqrt((b-a)**2/12)/np.sqrt(n)\n",
    "    xvalues = np.linspace(-3,3, 1000)\n",
    "    plt.plot(xvalues, pdf_func(xvalues, 0, 1), linewidth=2, color=\"red\")\n",
    "    x = np.sum(data[0:n,:], axis=0)/n\n",
    "    x = (x - mu)/sigma\n",
    "    inter = np.linspace(-10,10,100)\n",
    "#     inter = (inter - mu)/sigma\n",
    "    length = inter[1]-inter[0]\n",
    "    epmf_values = epmf(x, inter)\n",
    "    print(x)\n",
    "    plt.bar(inter[:intsize-1], epmf_values, width=length, \n",
    "            color='#039be5', edgecolor='black', linewidth=1, \n",
    "            align=\"edge\", label=\"True histogran\")\n",
    "    plt.figtext(0.8,0.8, \"n = {}\".format(n), ha=\"left\", va=\"top\",\n",
    "        backgroundcolor=(0.1, 0.1, 1, 0.15), fontsize=\"large\")\n",
    "    plt.xlim(-5, 5)\n",
    "    plt.show();\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 7.07732629e-02 -1.07745892e-01 -4.90864550e-01  3.33684114e-01\n",
      " -6.35670876e-01  9.05525862e-02  4.97468299e-02  1.39725580e+00\n",
      " -1.22948822e+00  4.05072869e-01  9.21873153e-02 -8.37684610e-01\n",
      "  1.18603825e+00  3.97054509e-01  2.50914097e+00 -1.29041834e+00\n",
      " -1.52857033e-01  2.21878861e-01 -9.93104100e-01  1.48011780e+00\n",
      " -1.73721739e+00  4.69496993e-01 -4.04414438e-01 -1.66013624e+00\n",
      " -1.62108914e-01 -7.98708794e-01  3.26109054e-01  9.38645023e-01\n",
      " -1.14852364e+00  1.41646368e+00  1.53890060e+00  5.21180529e-01\n",
      " -6.02021665e-01 -2.47624414e+00 -1.24557010e+00 -8.00116655e-01\n",
      "  1.54221371e+00 -4.28920698e-01  1.74110793e+00 -2.75199121e-01\n",
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\n",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean_hist_std(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean_hist_std(50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}