{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bayesian Statistics Made Simple\n",
    "===\n",
    "\n",
    "Code and exercises from my workshop on Bayesian statistics in Python.\n",
    "\n",
    "Copyright 2016 Allen Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import math\n",
    "import numpy as np\n",
    "from scipy.special import gamma\n",
    "\n",
    "from thinkbayes2 import Pmf, Suite\n",
    "import thinkplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The World Cup Problem\n",
    "\n",
    "We'll use λ to represent the hypothetical goal-scoring rate in goals per game.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compute prior probabilities for values of λ, I'll use a Gamma distribution.  \n",
    "\n",
    "The mean is 1.3, which is the average number of goals per team per game in World Cup play."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3103599490022562"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Zfclr8yqw1cw2A48CX/Ve3gN4y8xKgCXA6/WFfKKgz7qJN+26uuGb5Wu2se/QcR+rERH5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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff299db0cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from thinkbayes2 import MakeGammaPmf\n",
    "\n",
    "xs = np.linspace(0, 8, 101)\n",
    "pmf = MakeGammaPmf(xs, 1.3)\n",
    "thinkplot.Pdf(pmf)\n",
    "thinkplot.Config(xlabel='Goals per game')\n",
    "pmf.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:**  Write a class called `Soccer` that extends `Suite` and defines `Likelihood`, which should compute the probability of the data (the time between goals in minutes) for a hypothetical goal-scoring rate, `lam`, in goals per game.\n",
    "\n",
    "Hint: For a given value of `lam`, the time between goals is distributed exponentially.\n",
    "\n",
    "Here's an outline to get you started:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Soccer(Suite):\n",
    "    \"\"\"Represents hypotheses about goal-scoring rates.\"\"\"\n",
    "\n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"Computes the likelihood of the data under the hypothesis.\n",
    "\n",
    "        hypo: scoring rate in goals per game\n",
    "        data: interarrival time in minutes\n",
    "        \"\"\"\n",
    "        return 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can create a `Soccer` object and initialize it with the prior Pmf:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3103599490022564"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Zfclr8yqw1cw2A48CX/Ve3gN4y8xKgCXA6/WFfKKgz7qJN+26uuGb5Wu2se/QcR+rERH5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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff299ce8090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "soccer = Soccer(pmf)\n",
    "thinkplot.Pdf(soccer)\n",
    "thinkplot.Config(xlabel='Goals per game')\n",
    "soccer.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the update after first goal at 11 minutes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3103599490022566"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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1F1de3Cd6bO/Bo/zooRd5ZNLblJaW+VidSPMWqGRV0Ce3VlktePC7X+D7E0ZF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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff299cab310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Pdf(soccer, color='0.7')\n",
    "soccer.Update(11)\n",
    "thinkplot.Pdf(soccer)\n",
    "thinkplot.Config(xlabel='Goals per game')\n",
    "soccer.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the update after the second goal at 23 minutes (the time between first and second goals is 12 minutes).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3103599490022566"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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1F1de3Cd6bO/Bo/zooRd5ZNLblJaW+VidSPMWqGRV0Ce3VlktePC7X+D7E0ZF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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff299c7c0d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Pdf(soccer, color='0.7')\n",
    "soccer.Update(12)\n",
    "thinkplot.Pdf(soccer)\n",
    "thinkplot.Config(xlabel='Goals per game')\n",
    "soccer.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This distribution represents our belief about `lam` after two goals.\n",
    "\n",
    "## Estimating the predictive distribution\n",
    "\n",
    "Now to predict the number of goals in the remaining 67 minutes.  There are two sources of uncertainty:\n",
    "\n",
    "1. We don't know the true value of λ.\n",
    "\n",
    "2. Even if we did we wouldn't know how many goals would be scored.\n",
    "\n",
    "We can quantify both sources of uncertainty at the same time, like this:\n",
    "\n",
    "1. Choose a random values from the posterior distribution of λ.\n",
    "\n",
    "2. Use the chosen value to generate a random number of goals.\n",
    "\n",
    "If we run these steps many times, we can estimate the distribution of goals scored.\n",
    "\n",
    "We can sample a value from the posterior like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.04"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lam = soccer.Random()\n",
    "lam"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given `lam`, the number of goals scored in the remaining 67 minutes comes from the Poisson distribution with parameter `lam * t`, with `t` in units of goals.\n",
    "\n",
    "So we can generate a random value like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 67 / 90\n",
    "np.random.poisson(lam * t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we generate a large sample, we can see the shape of the distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.777"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff29a324090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample = np.random.poisson(lam * t, size=10000)\n",
    "pmf = Pmf(sample)\n",
    "thinkplot.Hist(pmf)\n",
    "thinkplot.Config(xlabel='Goals scored', ylabel='PMF', xlim=[-0.6, 10.5])\n",
    "pmf.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But that's based on a single value of `lam`, so it doesn't take into account both sources of uncertainty.  Instead, we should sample value values from the posterior distribution and generate one prediction for each.\n",
    "\n",
    "**Exercise:** Write a few lines of code to\n",
    "\n",
    "1. Use `Pmf.Sample` to generate a sample with `n=10000` from the posterior distribution `soccer`.\n",
    "\n",
    "2. Use `np.random.poisson` to generate a random number of goals from the Poisson distribution with parameter $\\lambda t$, where `t` is the remaining time in the game (in units of games).\n",
    "\n",
    "3. Plot the distribution of the predicted number of goals, and print its mean.\n",
    "\n",
    "4. What is the probability of scoring 5 or more goals in the remainder of the game?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing the predictive distribution\n",
    "\n",
    "Alternatively, we can compute the predictive distribution by making a mixture of Poisson distributions.\n",
    "\n",
    "`MakePoissonPmf` makes a Pmf that represents a Poisson distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from thinkbayes2 import MakePoissonPmf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we assume that `lam` is the mean of the posterior, we can generate a predictive distribution for the number of goals in the remainder of the game."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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B3kjS7mV0dJTR0dFWdduE+yZg/sD6IU1ZG5Nqu/iEU1ruVpLmnl6vR6/X27a+fPnyCeu2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\nldOXmOmaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff29cb8c210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lam = soccer.Mean()\n",
    "rem_time = 90 - 23\n",
    "lt = lam * rem_time / 90\n",
    "pred = MakePoissonPmf(lt, 10)\n",
    "thinkplot.Hist(pred)\n",
    "thinkplot.Config(title='Option 1', \n",
    "                 xlabel='Expected goals',\n",
    "                 xlim=[-0.5, 10.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The predictive mean is about 2 goals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.97549010518228874"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the chance of scoring 5 more goals is still small."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0032977689768040348"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred.ProbGreater(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But that answer is only approximate because it does not take into account our uncertainty about `lam`.\n",
    "\n",
    "The correct method is to compute a weighted mixture of Poisson distributions, one for each possible value of `lam`.\n",
    "\n",
    "The following figure shows the different predictive distributions for the different values of `lam`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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e8YpX4LWvfa2upyMIgrAXlkLclVKo1WpTeeqcn84DnYPBAPl8Ht1uF4lEAqlU\nCoPBAEoppNNpbGxs6LICHH3zYtjpdBovvfQSlFJ6gDadTqPdbmNlZQUbGxvwPA/JZHJqMhMPhPJM\n10l7dZpkMpnUy/iFYTgl9izoPOOVBZ/TLTmFst1u62wdz/PgeZ62lVzXxWte8xrccMMNc/s8BEFY\nDpZC3Ov1urZa2u02SqWS9td5oNN1XXQ6HWSzWURRhMFgAM/z9AQnzrJhD9x1XZRKJV2bJp/P4/Tp\n03rSE9eV4frvmUwGg8FgKnoHoHPczaid68GzH59KpaCUwnA41MLPM1nZpjGvAljwuWAZ3zc7An49\nF0e7++67ReQFQdAcmrgT0X0Afg3jGa0fU0r9kvX8+wF8cHK3DeAnlFKPx+xHtVotnYu+srIylfpo\n2jA80YkHTflx13UxHA5Rr9d1frzjOAjDUEfkLMo8qNrtdlEqlXD+/HkcP34c58+f11E/EWEwGOhI\nnF9r2jOj0UhH2uzVA5gSdjP6ZxHnToP3YZY2YMyBXB6UZb/+jjvuwOtf/3pJrxSEq5xDEXciSgB4\nGsDbAJwF8DUA71VKPWVs8yYATyqlmpOO4AGl1Jti9qV4QWxOfaxUKjr1sdPpwHEcPYDKET6Lr+u6\nCMMQ3W4X3W5X16FhX5x9+UwmA9/3tb3DA7Zs/XARMk6d5HRHO/Lmsgb8HABtIXGePb/eHGjlqN8U\nfgBT/+2cer4K4Xa32200m004joOTJ0/iLW95i0yUEoSrlMMS9zcB+JBS6p2T+z8PQNnRu7F9GcDj\nSqnrYp5TGxsbunIjlxlgayaXy2mB43VQzZrtPOkokUhge3sbURRNLbHHHcba2hqUUmi1WtrO4YW3\nNzY29EQnzqzhwmEs2By9s5/PVSh5UpTnedou4oqRLOwcZfNgLzBt9wC4SNT5vmnZ+L6PIAjQ7XbR\naDQQBAHy+Txuuukm3H777VK4TBCuIg5rEtM1AF4w7p8BcMcO2/93AD4768lyuYx2u41sNotut4tc\nLqcrOHY6HSQSCV2ml4uBsci7rquzZNgq4UicB1tXV1dx9uxZXH/99cjn89ja2sL6+roelPU8T9sm\nvBg3izpPhuLngfFJZTHv9/tTA73cAXE5YTNVkm/zYC//NwdjzYlUZmYOFzVLpVJ62cHhcIhut4tH\nHnkEDz/8sK45f8stt+DGG2/Ua8YKgiAABzxDlYi+D8CPA5hZTeuBBx7QQnbXXXfhzjvvRKFQ0D5z\nFEXaRjEBMgHzAAAgAElEQVT9cM/ztC9NREin01pwuYBYq9VCPp/XOfRra2vIZrN6gpRpA5kTpHjf\nZslfHtjlejLJZBL5fF6naHJeO5clNgdlOXVyNBrpRUlY4HmWKxcwM2e+co160wpKJpNwHAee5yGT\nyaBcLmM4HML3fZw7dw7f/e53AUBfwZRKJaytrWFtbQ2lUgmFQkFf+Xied5AftyAIh8SpU6dw6tSp\ny9rHXm2ZB5RS903ux9oyRPR6AJ8GcJ9S6jsz9qW2tra0D86e+WAw0NE6AHiepyNi13WRSCR0dMxR\n7fnz53W0jHGDUK1WEQQBCoUCzpw5g0qlAs/zcPbsWayvr6Ner+sIntMjeaGPfr+vo3eziBhnyLD1\nwrNo+bFer6cFmNM1ubok/zcnS5lePYCpTBxg2o83J0mxf882kZ16yemYvu/D9/3YGbeO42B9fR1v\nfvObZSlBQVgiDstzTwL4FsYDqucAPATgfUqpJ41tXg7giwB+VCn11R32pXzfn1oGj4iQSqV0tM6r\nNLHQsqCxZcFWR6PR0MvncR0ZLjfAg7Hb29tYXV1Fr9fDcDhEPp/XaZc8+xWAHmjl8sGj0QiJREJn\n3rCgVioVNBoN5PN5nTXD6ZUs0gC0pcPiapcSZsFnf55tGo7g7YVC+DV8hcDPA5i6z4PB5h9vA0BP\nrOLyx6urq7jtttvwmte8RmwdQbiCOexUyF/HhVTIDxPRBzCO4D9KRP8GwHsAPA+AAARKqYt8eSJS\nL730kk59zGaz2vbgNVPZygAuDEryoCXbJo7j6EU/uJBXOp1GrVbDtddeq8WYK0NmMhnwQG6n09ER\ntNmpmLYMR+Lm1QMvHpLL5fRVh1IK/X5f170JgmBq1qvv+zpKN8XfnOnKj3PWjZ1maWbvmNE8P253\nGmaHwMcyFwfngVr28LmTymazWF9fxxve8AacPHlSxF4QriCWYhIT53Jz1Uf2y9neYG+a/Wwe4DQH\nPZVS2NraQhRFelA1DEOUSiXUajWcOHFCp1Vy9gxH7zyAWy6X9XqtSqmpzBczMjYLjPHiIdxG7mg4\n8iciDIdDbYHwVYYZwTOmCJtVJ01RB6D3wZj3beG30ysn5/yi6J/PL1s6XI6BSxkrpfTs2fX1dVxz\nzTU4efIkqtWqiL4gLIClEPfNzU3k83m90hIX3eLUPq41w5ZJEAQAoJfEY/HjDBkWRfbcG40GPM/T\n0TRbNJ7nYXt7G/l8XgtYEAR6IW3OTOGJU3bHwvtg0eeB016vh3w+rzsqtli4EzCtETM656uHyXnR\nET53DJwSaQqz+VntlF5pXiGYVwzcMdhWDou+WSuHBZ87ArOzMJco5PfCC4h/7/d+L2644QaZeCUI\nB8hSiHun09ELaHS7Xe25c564bcGw9w1c8LJ5cNN8PQ+kZjIZvPjiizhx4gQGgwFc18XGxgbW19fR\n6/XQ6/V0hM+dAWeSdLtdANCpj2wLcXQ/Go20p59KpfTqUJzayeLIdeZ5cQ/+M31wFkQWcL5q4fdt\n2jO2nWNn59iTqez8ecaM7nm/ZuEzcwat6fGbJY7NToWf4w6k3+/r8RHP87C6uoqbb74ZN998s+Tl\nC8JlsBTivr29Dc/ztB8OQC9yzRErCwhHwiw0pi3T6/WmJhQFQYD19XVtN3S7XVQqFR3ls+CwEPOg\nYr/f1z46e+1mR8PpiaPRSI8VsKXE67pms1ltKyWTyakiaBwlc5Rriqj5GFshZlYQX7UAuEjgWUTN\nz8+2Zibn/CIPnrcxrwy4nbbNY943227vjztk9vV930ev19PHcBwHqVQKpVIJ1157LW644QZce+21\nkp4pCHtgKcS92WzqAdTBYKAHNoELA6gcrdtCb9ZWV2q86AdwQejW19d1MTCeicqWyvnz51GpVABg\nynPnMgRm9M5XA2amTjqdxnA41AXK+H+5XNZ589yJcAdhWkYcxbPvbhcnMwXe9O3Nc2JG62ZVStOa\n4Yjf9vntyJ6FnLc1RZvbyo+b+2PM7fk9cwfB1o8545YXNOEBXb5y4M+VS01wPn8+n0c2m0U2m0Um\nk0Emk8GJEydQKpXE8hGuOpZC3Le3ty8aQOU8bTP90azRwrYMP8biX6vVtGilUimdGeP7PohIWy/J\nZBLdblfbKizGHGFzDZpWq6WLkbEIccQ5HA51yV9zVi1PauJaN7bfzrcBaNHj9rPImmmephdv++1s\n4wDTfroZWZsZN6Y9Yws/H9e0aHi/9hWA2YmY+2chzmaz+v3GWTxm1G8XUIvrCNgqMt8374Oj/+PH\nj+O6665DtVrVV0mCcFRZCnGv1+vwfX/KTgEuLFrNEaVZ34WFAJiO6re3t7Uwslefz+d1PZpmswkA\neuYrz2AFgGaziXK5jFqthnK5jF6vhyiKdITOEb9Z06ZSqegBV7Z4eHYtlwhQSmm7h6NS7mxY0Fmg\nzU6LSy10u13dBt6Gz5Htw5uToszBWeBCx2Cce90hmOmUvD9+jT0Ya+bks5hzhpK5b37NrOyduLRO\n88rAfNw8vrmdKf6cNuu6LvL5PFZWVnD8+HGsrKyI1SMcOZZC3Gu1mi7byznlLGDmrE3TqmCxNz14\npcaLXrNgciZLLpfTVsRoNNIeO/v5rVZLV6BMp9Po9/vwPA+9Xk9H4AB09D4ajbRd0Ov1dEdAkyqV\nXB+Hc9+5wzLLA3POvO2zm1E8X7nwQC3bM5Pzpu0hM7Ln52yLxBRPfg0fO05MTVHl881XLOaCIuZ2\n5nH4M5sl3Pa+zfv2FYO5L8bsIMwrA3O2rnk+s9ksisUiqtUqqtXq1HdCEJaRpRD3RqOhc8o5Ajez\nYMwo0PSN+cdpRqitVkt3EFzuN4oilEol7RtHUaRrxwPjiJ3Fir3zZrOpbRpejJsHBblG/GAw0FUs\nq9Uq2u22tlJ4IRCOLh3H0evBcqRpWjOmz84dF++LOzo+D1yPxhxUNsXeFmgzM4fPqWmnxNk4vJ3r\nukin00ilUjpv3xTpOIuHH4/z5mfZO7OeNy0Y01Kyr1hMG8m2fcwOhN8fF18rFouoVCrI5/N6nEcQ\nloGlEPeNjQ09u9O0G8wftem1xk384cfr9TqUulD7JZPJaMEGLsz+5EFSriPTaDRQrVZ1jRgWX47C\nOb+bUyDNwmEAdPTfbrd12iMAbRPwrFVeWYorWbKIc4fGVy38fjOZjF7nldMtzVm6pujzeYoboDU/\nU1MgTbHmAcx0Oq3LPvB+zfPN+zCfMwXXtNBmReV2Z2I+Zx7LbKv9/KyOwp7wZV8x2Nk9/L1Ip9PI\n5/PI5/MoFotIp9MS3QtXLEsh7s1mc6r2OfvOdpqdmR9uR4/8I2y1Wlrcud654zg6M4aFVCmlZ8UC\n0IO5PLGpUqnoqpQ8kJrNZjEajTAYDJBKpbRdwgtmcATfaDT0otss4ul0WqdI8nvlNvKVBqcOAtCD\nkUqNyxazsHP0z7Vr+DXmVYwtlqY4ckcIQNsV/F7M826K6U77MqN183MyX2d/Xub2cfvm45tXGnHf\nSfv1/P7NtsTZS2b77DaZ79t1XRQKBZTLZZRKJZmJK1xRLIW4b2xsAIC2IdjKMLa5SETiBD+KIr0i\nEme8VKtVEI1LAHQ6HZ0KyT41R9wAdBpjp9PRGTupVEpH7yzyZjEzLhdcLBZBRGg0GqhUKjqlkmfD\nDgYDZLNZ7etHUaRTNJW6MKDKJYXNwVszMmX7hVMiTevHzLYxrRpgWiA9z0OhUEA6nY6NwBk7ndJ8\nzt4+LrLmx20BjYuc4yL3vXwPbR/e/rOfiwsM4t6H3Tkkk0kUCgWUSiWUSiXJxhEWzlKIe61W00K0\nm6gDmIq+7EieJ8ywQK6urmrxZHFmKwWAzmfnSJsj9Hq9ris+csTOEbhSSgtrNptFMpnUAq/UeLUn\nzpkvlUo6NbLT6eh1YDnF01wu0CyCxhE5L9zN0TpvxwOuAHQ6pD24ambMcJTOlTJNu8GMlm0R5PNu\nR/P2a+P2NWvf5uc5S9TjtjePb18dzLpt7se2eczv1KzH7E6Mr3x4jQARemFRLIW4b25uXiTqJnGX\n7gCmvGVzW85fB4CVlZWpHzqvQZrJZPQ+ecEO9uyLxaIW3TAMdYqjuVi367pTs1mTyaROfwSAdrut\nlwrk3Hf23Dk3nvdt2jTcEbH48/KC/X5f++08OJtOpzEYDKbSKc2FQjjTJp1O6zZyZM9ZRixWfDXD\n59PMTtnJktntuxIn1HaHYD8X1wlY35mpAWH7SsDsNOwsG8a+KonL9LFtm7jOgztNFnoeJBeEw2Yp\nxP2ll14CMG0dxEVPxmtmRl4s0CxQlUrlosyOWq2mPVQWxW63i1KppG8Xi0Vt07CHrpTSUXQikdCz\nU3kQNpVKodVqIZPJgIh0vRzeD4s/WzUAdIE0pZT2znmgFIDe3s5/59ucSWMOwvJEMK6rY4q9GeWz\npWMKIHdocTbMLHtmVkRv2yB2KWPz87Oza+J8/biofbcrAjvCNx8DMLMts56LS8c0X5fJZFAsFlEq\nlST7RjhUlkLcz58/DyB+gM38AZuX+vzfFCV+nDNmPM/TaYsMiwvbLvwaXjibBZqtGLZ6uBgYT4Zh\nW4ZTKNvtNgDo6pa8JCBXiOQFQdiaMStd8uQms0QBR/F8LpLJJIbD4VTWDHcGLOr8fovF4lSevG3V\n8DlgO4HPrTmQOStC382eifusTJE0b/PYwKzI3RbnnfzxnUQ+7srB3I95m6Nx+/hm5pG5b/v1ZlvT\n6bQIvXBoLIW4b2xszBR2M5o3BcP+4bFFQ0TY3t4GMJ6FyqLH8H5Ho5GuBsmPcYSt1Ng354FRzmU3\nB1JZ2Nlm4Ro0o9FoalWnRGK87J45a5UtliiKdN68WUYYgLZ+2I/nQV07a6bf76NYLCKVSqFQKGjb\nxawvz1coZk68WeLAnNFqWzT2ldFOwm98phcdy8ytB6aFfVb0bHco5v5nib9ppdidP+/L3v9u78P8\n7ti3zfNifzfN7zB/PqVSSWbLCgfCUoj7uXPnYqO7OFEHpqM4a18AxpF7IpFALpdDs9mcsmAYpcbe\nvFJK++RBEGjB54wZADoHnWek8oSefr+Pcrk8FbUPBgP0+32USiV0u11thbA3b5YS4Hx3nn3KnY5Z\nooBfw8LOnjoPAhcKBR31s+Dzvs00SbMGjSn27Plzpcu4UsF8vsxzZ962hdt83ryimiXy9uceJ5Zx\nUbcdYdvfIbONce/H/A7FCbv9mP0eZ4n9brDQcy69IOyHpRD3s2fPzry0Nra76AcZF8ERjdMReaGN\nZDKpLRFzoWtz20wmo6Nk9swdx9H57jwoyjNQObURgM4+6ff7GA6HKBQKU769OWmJa733ej1dGoE7\nDXONWJ6YxIJdLBb1pCu2gXglqUwmo68ETPE2C5WxNw9ACzhH6GZnEVcHnokT7zhxi/ucbEyfP07k\nzX3FRdr2ffNKwRxfsF9rv4edxD3umHE2z6wrAPvKkh+3r0Qdx0Eul0OpVJpKTRWE3VgacQdmi8Ys\nYbe34e3MFZAymQzCMJwSePMYPDuVo3u+Xy6Xp9ZL5VmhbL+YtWW41spoNNJXCmztFItF9Pt9ABf8\ndRZ47lDMsgRKKZ3uGIahvgLI5XJYXV2F7/tT2Tcc9fPArCn0SikdkQO4aNDVPG/2+Z9lWcyK4G3i\nxDPOspjlycftO86G4dfEXXHs5MnHHSPuObsTmtXWnaL8uPPBxzG3SyaTuiRCNpsVoRd2ZCnE/cUX\nXwRwsXDsZr/Mgotz8UpMAPQgKtsYvB818ag5N53F1vd9PTjKYprP5/UCHmbRsG63iyAIdJ57o9HQ\nqYcc9fu+r6f48wxXs/olP6aU0h0KdyCVSgXZbBatVkvXuzEnKbGAm1Ewd0imPWNH7yz25uCsPaga\nN1t1L5+R+VmZr5+1SpRdbdL2zc392CLP78Ns10774MHR3eykuOg77nYccZH9rOPEXWmwrchCL2UQ\nBJulEXdbPHZqQ1wEZP4QubokR7m8P6XGVSMzmYzOXuDjBEGgBycBTOWss/3BVoxZ3ZEnMXG1yXw+\nj2Qyqa8eMpkMGo2GLjscReP641wojW0Efox/1LzmK++fhZ1LD/OKT9zh8NUA+/lsQbH1YkbyXHCM\nr2I4S8ecIGWL8G6TnOKEF4gvHWBuZ2fMxA3ozorYzSsTs47NTp0Ht8nsSGZF9Pb3yu407O9p3BWC\n/Zz9vTVTRG2bybRyuKplPp8XoRcALIm4nzlzBsDsSSJ83/6xxUVFAPQyemxr2PtutVq62qGJXUys\n1WqhWq1qoeda7Z1OR2/HC3KYr3FdF9lsFt1uV5cc5vK/AKasHrOKJNcdd11XWyupVAq9Xg/FYlHP\noOXMG17wm8WBxZJz3zmrhi0q02/nSN8s+cCdVNzg6k4RvHnf9pW5o7Aj1Dg7xp5wFCd2tmDPsnZm\nTV7i92pOgJuVjmlfdexkyexU/2bWY6Z4m6mWcdaX2aZcLod8Pj91FSpcfSyFuJ8+fRrAxRkIO0VR\n9o/Ajop4UQ62Shi+zZE1p0uawm8Okio1LtzFkTPXdudIPp/PTw2mcmaM7/uxg6ssqP1+X3cuhUJB\nL/rB+fVcwyYIAu2722mWbCFxR8KDq5wxY058siN2vs1jBQyLPHcSpt1jf0Zx0aj93eFxDFPc48Se\nP8M4z90W0J2sIFPs40Qz7ju116jd3L99BRPXycSJtclOdpfdPu6Q7ajdFHopg3B1sRTi/vzzzwOI\nF3d+fJa428LDj7daLQDQnnvce+L1Vtl+Ma2bUqmERCKBZrOpUxxZlPP5vI7y2TaJokhn02QyGQRB\noG0TItKTl3iglCtUVqvVqYlLvMA3CzeXIVZKaWEnIl1lkvPmOa+do3fOumGrxfTozfxz7kD4PcSJ\no3l+d7ttE5d9EyeILF480GuL3iyRtPPz+XizfHhzf7b9Y3ryZtQ+K5o2b5vfxbgIP+7927fjztMs\nrz+ug+N1ZovFopRBuApYCnH/7ne/e1FEFhcJzYrWjH3pH0ej0dBepX3JbN5m+4aLiSmltK1TKpW0\n1cJ1YrjSIwA9iYmvAIDx5CPOaecJTGzh9Ho9rK6u6oVD8vk82u227gw475z3yT48LyzRarX0ZTmX\nPFBK6Trz7Lnz4CwPqLKocweg1AXvnUXdHpQ1z3/ceeP7s0TNFEvzczTtH9OysaNg83j294Cfs4Wc\nBd4eMzBfY0fDtk8PTI8T2DaSTVzkHfd8XAcxqwOxz8Gsshy2ncQQjZc/5Nr0kmJ5NFkKcX/22WcB\nzPYnzS9mXMQeR6vV0uuozvIl+XiDwWAqs4ajZl74mlMZWZRYTNmKGQ6HUymRURTpapPcuTiOg+uv\nvx7dbhdRFCGbzU5l4ph2DFs+SiltEbVaLZ0qx7c50s9ms/rKwrY84qJ3syQwY1owe4lS4543MSNW\nM6qe1UHwebe3MyPsONtj1uCvGbnHWS32lQNwcdqj+Rq7A4gLPkz/3nxvdidjtn/WvII4wTfbY55n\nc1zKhs9/JpNBJpNBLpcTsT8i7Efc527cKXVxfW37/k5fdr5v+pF831zIwr4y4P8cAXO+u1JKr+nK\nHrbpubMtw6UIuEjXYDBAvV5HNptFoVDQi0YfO3YMjuOgVqvpDiSuLDAXJ+MInKPsZrOpB21brRYS\niYS2ZXgyFL9fs5yBuSyeOfjI55ctkLgJP3vpQJm4qNM+z3FRO/83vfhZwg5cXItmt8jd7OTirgjM\n70kURVNXMmZnMitCNr9/Nnbkb59b8ztpn+u4cx/XKdnnOW4//NfpdPR3h4MOLgHNNqBw9Jl75P7M\nM88AiPdFd5oMYm9r3ucSvaYwzspJ5v2a5QcYXktVKaUHQc1Vm/r9PqIoQiaT0dG067rIZDJYWVmB\n4zhoNpuIogiVSkWv8ZrP57G9va2rTvIMWI78WaS55G8ymdRZOvai3VwSgQdJbeHkcxYnjgAu2i5O\nyGxxnBUFm/veSYB3s39ssY+zHszHbO99L8eL+67xvuzgAYhfoWqWrWJG1Cb2lQefn71G8LPeg91h\nmOdoVpv5NZx+m81m9VqyIvZXPksRuZs/7FkeadwlOWP+gHlbFjPOUqnVarrAlx3x8G0zL71QKICI\npiYyEY0nRnFkz1E8tyWXy2F9fX1qXValFMrlMqIowubmps6o4aqU3Hnw4Civ1MSTnSqVCoIg0Nk9\nLOxs7QyHQ33pPRwO9UpO9gCjfd74sVk507Z47OYNz7Iv+HHel5mFY2blmJ+xnVETt0/TqjE7Ljty\nn3UO4t4Hb2fbO7POg30OgAtXF3FpmnYnaBIXkdsdn90J2r+TuP2Yv6k4keeAoNls6nGqRGK8GAln\n4khFy6PD3CP3J5544qLHzcthO3KfvE7/j7uM5ZK6Zj0Z3/d1PXauoR5HGIZot9ta0HmAtVAo6Jmq\nHC2Xy2Vce+21en/tdhuDwQC5XE4v7tFoNOA4jl5A2/f9qTrxPPBpLqZtdkLsm3N5Afb8oyjSi3Zw\nBcjdJiSZ59EUx1liY3ec5mcwKwo2nzMHdM31a00htm0aW5DjBNL8DvBtO+XSvL9TBD6r7Tb2ObIt\nm50i5LiORakLZSDs/cXdj7uijbvyiDuWfV74eTMIMM+Nieu6enA2l8uJ2F8h7Cdyn7u4P/7441OP\nmcIT92WbvG7qx2aLPA9Osp9ubj8YDHQ9FzuS5+PzoCgPaHJnUS6X9X+2a7g4WD6f1+Vcu92uHmQt\nFArwfV9PPEqn06jX69pjZwuGSwkD46wbnsjEdeZZ2Ln0sFkHniczzYqObWE0xdcWHz6f9utm5ajv\nZs2YZQ9Y4M1j7CTss6w087OPex2AHcXd3E9cZM/ttqN289izRNg8v/Zj9nd3Jxtm1tVF3OB03PHM\nq4+482pbVjvty9wnjzFxJg5/H4X5shTi/uijj150CQpcnC5mvGamtcLPAxd8d/NS29yexZJXUTLh\n4/m+j/X1daysrOiMGo7+2+02jh07BmD8A+eo3HEcvWDGYDDQ+e+lUgmDwQCdTgeFQgFhGKLf70/V\neuc89zAM9exWFnKOzNmyiaJIe+3mRCU7oo6LenkbM6/cXJfVXqPVFOFZWSN2aiHvJwiCqXIIpsc/\nK089TtjiRM8WuZ38a/NzjYu64zJl7NeZt+ME2MaOrO0xD7Nzsc+nfQy7czUDoFkZM3GW5awrLvsq\nI+69mB0nt5+z0tLpNNLpNLLZrC7xMWtfwuWzFOL+N3/zNwDifzS2wJtfdFOs7EwZIkK73dYzUPlx\n+0fKkXMQBEin0zpdrFwuo1wuw/M8bG1toVwuw3VdbG5uolqtYnt7W2fNcB46TxxhjzwMQ6TTaeTz\neV0xkoh0pUhOpeTa8Ry9sq0yGo10miO/Z37c9HZZhOM6R/M/cLElYea+m2us7mSn8GNxto8tVtxG\njtZZ7G0bwLYM7PcQ935sa27Wa2ZZErOiU1uQ4yZW7bTPWVc19sQquyOJE3bz+bi2x10F2L+JuHbb\n54c/i7i2zWpLXOdnBlCO4+g1fPl3ZZbXFi6PpRD3r3zlK1qs475gdrQVF4XERe88OGnuw45OiMaz\nPVnIHcdBpVKZqjuj1Hjd1Xw+D9d19RqsvV5PD3iai3Jz9MKpkuZM2FQqpbNnuHQBR+DmIth2VE10\noQ6MGVHz87MiPj5nHHHb/qrZIQEXxJ6vEqIompoAxR1t3GV+nGCa2SD8+drCbot23H5sceXPLk5g\ndorkbZvFfjzuu7TT1YBpe8wSdrN99neaz1FcZtCs32Hc1cgs68g+v3EWGj+305XMrGPGtWnWb5OP\nwdVOM5mMTsdk0Rf2zlKI+5e+9KXYH3Kcrzh5zUURPT9vRiucL25Hg6lUCsViEZVKBaurq3pBa35d\nu93WUbUp8rVaTac8cvmBRGKcc86XoEqNF9Hu9Xq6PdlsVhcAY5+cJ0eZk5bM92IusAFA32YRNc8J\nv87OqrCjNH49/+f3zCs/8SxZrlFilirgKD3uxx8XdZtiabYvLrXR3t8scePt7IqOcVZBXEdgdnR2\nzRtzH6Zo8f52spPizsOsFMxZVwpxA6fm83FizO/LbI/JTkJv7tdu36yxFPtzmPWcuY39fuJ+w/yd\n49IdnJLJwdBOExGvZg5N3InoPgC/BiAB4GNKqV+K2eY3ALwTQBfAjymlvhGzjfrc5z4X+wWwtov9\nMpnP2fc564TFtFqt4tixY6hUKrt+WZQa16fhssE8UFqv1+G6rm4HlwjgxTwAaP/R8zxEUYRer6cH\nZFOplM6P5ywY4MKaqZw5w0Jp1543I1/TX2fRUurC5T//aOKW0eN9mh2AacsAF6LuOD/d9n5nCbQp\niPb5tSP+uEgxTtTihIjfj9mp2OJqH9e2Mcy22YEFgIveq/3auM7UFjlT3MxtbGwRn9UB7BSNm1en\ncR2vfc5mnfO4cxDXUZjnYVY749pg7sN8n/y84zhIJBJ6DglbPRz9c2IEb3e1sB9x3zXPnYgSAD4C\n4G0AzgL4GhH9kVLqKWObdwK4USn1KiL6uwB+C8Cb4vbHtgUQ7wuab8a2Hfhx9nZZPNPpNHK5HF72\nspfhZS972SWvbENEUysq8apKnJtORPB9H6dOncK9996rc9M5yh0Oh3qNVgB60hNwoZ4NfxHZ7uD/\nLHgs1Cy4phBydM0Cz2V9wzCcKsDFFg//Z0uHz+NDDz2EO++8Ux/D/GFzZ8H7tW/zfuzPxRRcexER\n4EI0bP7AzciY9xMnEOb+E4kEHnroIdxxxx1T4jJLrGb57WbEbx4vTnzMdpiiHWfD7HQVwo89+uij\nuPXWW6ces8XXPte2qJrt3+lKYS8BVFxHPOu9PP744/ie7/meqXNrd7o7dRRxnWTcb9QOauzzz50N\nZ465rqsFn3WAyy/wlUAikcCpU6dwzz33XHS8o8xeJjHdAeAZpdTzAEBEnwRwP4CnjG3uB/A7AKCU\nepCISkR0XCm1Ye+MZ23O6u35g0smk7pWOueR80LD+Xwe2WwWruvqLwGnHl6Ol2eKfLPZ1EXEOPXw\nwZsrL/8AAAr3SURBVAcfxL333quzYuwvMX/h2PZgkeb3xxUhzYFR/jKbX2rTNoiiaKoomFIKw+Fw\nKurhQUtTLOyBOqUU/vqv/xq33Xab3g642MtnbBGL+7z4f1ykaUeY9o8/TghnPcave/DBB/G6173u\nomOY2zG2fWKe37hBTH4P9r7tqNO+4jA/TzPKjROwBx98EK961atij2FuG9exxAlm3DZx9oh9fuPO\n36wrFb798MMP44YbbtjTvuI+47irjN06oLhzaGqHeRw7xZUDQJ5J/qlPfUpf1fLKZ+bVgfnH6yyw\nRWT+JpeJvYj7NQBeMO6fwVjwd9rmxcljF4n75uamFnAejOQa1dVqFSsrKyiXyzojZa8nla2Igxio\nISKUy2Ut8mypcNGwuO1ZQHzf19GumeUCQAs+v4YXx7ZzzPlLamcF8Rc7bqKRKVj2ZTlvNxwOde17\nboPt3dr73IuwzxIz87k4a8Ped5y4m9v2+33UarUdRZ3fs/1ae5tZwmJ2RrMskJ38+7i28+Pdbhe1\nWu2iz8+OouMGz+0r3Lhzam83633Ztltcp2hfTfDMb/N82qJrvhfeblanb39P7O3jBNzuvOLOi/1+\nmVqthieffPKi9vL5tq8WuB18lWx2Fhx48tgBdxLcGcTd5j/zvuu6en9mR8KdyeV2KHMvP/Cud70L\nx48fR7lcPtAFB1zXxfb2tq7qeJAQEer1OgaDwZQ4MqYom1G4/R+AjubZUgnDEEEQ6GX5zH3Giasp\nMOaPiDsUux3m8c6cOYOvfvWr+jWmMDH2Me328G2zPXuNwGY9Fne8OM6ePYtHHnlk1+2uVOr1Or79\n7W8vuhn7ot1u49y5c4tuxr4ZDAZoNBqLbsZc2XVAlYjeBOABpdR9k/s/D0ApY1CViH4LwF8qpT41\nuf8UgLuVZcsQ0e6/YEEQBOEi1CEUDvsagFcS0fUAzgF4L4D3Wdt8BsBPAvjUpDNo2MK+n8YJgiAI\n+2NXcVdKhUT0UwA+jwupkE8S0QfGT6uPKqX+lIjeRUTfxjgV8scPt9mCIAjCTsx1EpMgCIIwH+Y2\nC4CI7iOip4joaSL64LyOexAQ0bVE9BdE9E0iepyIfnrRbbpUiChBRI8Q0WcW3ZZLZZJa+++J6MnJ\nZ/B3F92mS4GI/jER/S0RPUZEv0dEV3QdXSL6GBFtENFjxmMVIvo8EX2LiD5HRKWd9rFIZrT/lyff\nn28Q0aeJqLjINu5EXPuN5/4nIoqIqLrbfuYi7nRhItQ7ANwC4H1EdNM8jn1AjAD8rFLqFgB3AvjJ\nJWs/APwMgIuL6S8Hvw7gT5VSrwXwBgBP7rL9FQMRnQDwjwDcppR6PcZW6HsX26pd+TjGv1WTnwfw\nBaXUawD8BYB/OvdW7Z249n8ewC1KqVsBPIPlaz+I6FoA3w/g+b3sZF6Ru54IpZQKAPBEqKVAKfWS\nmpRTUEp1MBaXaxbbqr0z+VK8C8D/vei2XCqTCOstSqmPA4BSaqSUai24WZdKEkCOiBwAWYxnel+x\nKKX+CkDdevh+AP92cvvfAvihuTbqEohrv1LqC0opzvn9KoBr596wPTLj/APArwL4ub3uZ17iHjcR\namnE0YSITgK4FcCDi23JJcFfimUcYHkFgC0i+vjEVvooEWUW3ai9opQ6C+BXAJzGeHJfQyn1hcW2\nal8c4ww4pdRLAI4tuD2Xwz8E8NlFN+JSIKIfBPCCUurxXTeecPVU3jkAiCgP4A8A/Mwkgr/iIaJ3\nA9iYXHnQ5G+ZcADcBuA3lVK3AehhbBEsBURUxjjqvR7ACQB5Inr/Ylt1ICxjoAAi+mcAAqXUJxbd\nlr0yCWZ+AcCHzId3e928xP1FAC837l87eWxpmFxS/wGA/1cp9UeLbs8lcBeAHySiZwH8PoDvI6Lf\nWXCbLoUzGEcsD0/u/wHGYr8svB3As0qpbaVUCOAPAfxnC27TftggouMAQETrAM4vuD2XDBH9GMb2\n5LJ1rjcCOAngUSJ6DmP9/Bsi2vHqaV7iridCTTIF3ovxxKdl4v8B8IRS6tcX3ZBLQSn1C0qplyul\nbsD4vP+FUuofLLpde2ViBbxARK+ePPQ2LNfA8GkAbyKiNI3rPbwNyzEgbF/lfQbAj01u/zcArvQA\nZ6r9NC5b/nMAflApNVxYq/aObr9S6m+VUutKqRuUUq/AOOD5O0qpHTvYuYj7JGLhiVDfBPBJpdQy\nfMEBAER0F4AfAXAvEX194v3et+h2XUX8NIDfI6JvYJwt878vuD17Rin1EMZXG18H8CjGP9iPLrRR\nu0BEnwDwZQCvJqLTRPTjAD4M4PuJ6FsYd1AfXmQbd2JG+/8VgDyAP5/8fv/PhTZyB2a030RhD7aM\nTGISBEE4gsiAqiAIwhFExF0QBOEIIuIuCIJwBBFxFwRBOIKIuAuCIBxBRNwFQRCOICLuwkIgonCS\nb8zzBv7JHI5ZIqKf2MfrPkREP3sYbTKO0T7M/QtXH3NfIFsQJnQntWLmSQXA/wDgX8/5uHtBJpwI\nB4pE7sKiuGiGHREVJwu6vGpy/xNE9N9ObreJ6P+YLHrx50S0Mnn8BiL6LBF9jYj+I5cpIKJjRPSH\nk8UZvk7jtX1/EcCNkyuFX5ps9z8T0UOT7T5ktOWfTRam+BKA18S+gfGxv0JEjxLR/2pG30T0L2m8\nsMujRPT3J4/liOgLRPTw5PEfjNnn+uR9PELjxT3u2vcZFq5ulFLyJ39z/8N4AZRHMJ6W/wiA/2ry\n+Nswnnr9wxgv0MHbRwDeO7n9LwD8xuT2FwDcOLl9B4AvTm5/EsBPT24TgALGlRkfM/b5/QD+L2Ob\nPwbwZowLkz0KwJu87hmMF2ux38MfA/j7k9sfANCa3P4vAHxucvsYxosrHMe4rnt+8vgKxmsc8L74\ntT8L4J8abcot+rOSv+X8E1tGWBQ9FWPLKKW+OIl0fxPA9xhPhQD+3eT27wL4NBHlMK6w+O8nRbkA\nwJ38vxfAj072qQC0Y5Ym+3sY10t5BBMhBfAqAEUA/0GNC0wNafbShHfiwqIznwDwLye378K4AieU\nUueJ6BSANwL4MwAfJqK3YNxZnSCiY2q6ANTXAHyMiFwAf6SUenTGsQVhR0TchSuKiUi/FkAX4+j2\n3IxNFca2Yj2uk8DePGwC8ItKqX9jteFn9thc8xg7FXLi534E4/f0d5RS0aR8a3pqh0r9JyJ6K4B3\nA/htIvoVpdTv7rE9gqARz11YFLPE8GcxLun7fgAfJ6Lk5PEkgP9ycvtHAPyVUqoN4Dki4sdBRK+f\n3PwixoOnvDh4EUAbY5uF+RyAfzi5AgARnSCiNQBfAvBDROQRUQHAD8xo61eNNpnrov4nAD88Oe4a\ngLcAeAhACcD5ibB/H8Y20dT5IKKXT7b5GMbLIi5T7XrhCkIid2FRpA07RGFsWfw2xkugvVEp1SOi\n/wjgnwP4XzCO5O8gon8BYANjTx4YC/1vEdE/x/j7/EkAjwH4HwF8dDIgOwLwE0qpB4noyzReVf6z\nSqkPEtFrAXxl4uq0AfzXSqmvE9G/m+xnA2NhjuMfA/hdIvoFjDuKJgAopf7DZAD3UYztl5+b2DO/\nB+CPiehRAA9juq47XwXcA+DniCiYtGdpau8LVxZS8ldYCoiorZQq7L7l/CCijFKqP7n9wxgP+P7n\nC26WIACQyF1YHq7EKOR7iegjGF991DG+6hCEKwKJ3AVBEI4gMqAqCIJwBBFxFwRBOIKIuAuCIBxB\nRNwFQRCOICLugiAIRxARd0EQhCPI/w/qrY6uvHljbAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff299dfdad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for lam, prob in soccer.Items():\n",
    "    lt = lam * rem_time / 90\n",
    "    pred = MakePoissonPmf(lt, 14)\n",
    "    thinkplot.Pdf(pred, color='gray', alpha=0.3, linewidth=0.5)\n",
    "\n",
    "thinkplot.Config(xlabel='Expected goals')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compute the mixture of these distributions by making a Meta-Pmf that maps from each Poisson Pmf to its probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "metapmf = Pmf()\n",
    "\n",
    "for lam, prob in soccer.Items():\n",
    "    lt = lam * rem_time / 90\n",
    "    pred = MakePoissonPmf(lt, 15)\n",
    "    metapmf[pred] = prob"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`MakeMixture` takes a Meta-Pmf (a Pmf that contains Pmfs) and returns a single Pmf that represents the weighted mixture of distributions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def MakeMixture(metapmf, label='mix'):\n",
    "    \"\"\"Make a mixture distribution.\n",
    "\n",
    "    Args:\n",
    "      metapmf: Pmf that maps from Pmfs to probs.\n",
    "      label: string label for the new Pmf.\n",
    "\n",
    "    Returns: Pmf object.\n",
    "    \"\"\"\n",
    "    mix = Pmf(label=label)\n",
    "    for pmf, p1 in metapmf.Items():\n",
    "        for x, p2 in pmf.Items():\n",
    "            mix[x] += p1 * p2\n",
    "    return mix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the result for the World Cup problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mix = MakeMixture(metapmf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's what the mixture looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff299ea3ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Hist(mix)\n",
    "thinkplot.Config(title='Option 2', \n",
    "                 xlabel='Expected goals',\n",
    "                 xlim=[-0.5, 10.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Compute the predictive mean and the probability of scoring 5 or more additional goals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}