workshop01_soln.ipynb

{
 "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": 1,
   "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": [
    "Working with Pmfs\n",
    "---\n",
    "Create a Pmf object to represent a six-sided die."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "d6 = Pmf()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A Pmf is a map from possible outcomes to their probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for x in [1,2,3,4,5,6]:\n",
    "    d6[x] = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initially the probabilities don't add up to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 1\n",
      "2 1\n",
      "3 1\n",
      "4 1\n",
      "5 1\n",
      "6 1\n"
     ]
    }
   ],
   "source": [
    "d6.Print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Normalize` adds up the probabilities and divides through.  The return value is the total probability before normalizing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d6.Normalize()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the Pmf is normalized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 0.166666666667\n",
      "2 0.166666666667\n",
      "3 0.166666666667\n",
      "4 0.166666666667\n",
      "5 0.166666666667\n",
      "6 0.166666666667\n"
     ]
    }
   ],
   "source": [
    "d6.Print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can compute its mean (which only works if it's normalized)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.5"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d6.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Random` chooses a random value from the Pmf."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d6.Random()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`thinkplot` provides methods for plotting Pmfs in a few different styles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEACAYAAAC9Gb03AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUscZ9JLUcQa9JHXc/wfKPgVBfzMnfAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8134207190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Hist(d6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 1:**  The Pmf object provides `__add__`, so you can use the `+` operator to compute the Pmf of the sum of two dice.\n",
    "\n",
    "Compute and plot the Pmf of the sum of two 6-sided dice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAEACAYAAABfxaZOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nHyNPMQvJFWOvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8106cdd750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "thinkplot.Hist(d6+d6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 2:** Suppose I roll two dice and tell you the result is greater than 3.\n",
    "\n",
    "Plot the Pmf of the remaining possible outcomes and compute its mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.393939393939394"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAEACAYAAABfxaZOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nL0kNMfqS1JD/BRvbyHla71dWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8109484450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "pmf = d6 + d6\n",
    "pmf[2] = 0\n",
    "pmf[3] = 0\n",
    "pmf.Normalize()\n",
    "thinkplot.Hist(pmf)\n",
    "pmf.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cookie problem\n",
    "---\n",
    "Create a Pmf with two equally likely hypotheses.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bowl 1 0.5\n",
      "Bowl 2 0.5\n"
     ]
    }
   ],
   "source": [
    "cookie = Pmf(['Bowl 1', 'Bowl 2'])\n",
    "cookie.Print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Update each hypothesis with the likelihood of the data (a vanilla cookie)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.625"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cookie['Bowl 1'] *= 0.75\n",
    "cookie['Bowl 2'] *= 0.5\n",
    "cookie.Normalize()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Print the posterior probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bowl 1 0.6\n",
      "Bowl 2 0.4\n"
     ]
    }
   ],
   "source": [
    "cookie.Print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 3:** Suppose we put the first cookie back, stir, choose again from the same bowl, and get a chocolate cookie.\n",
    "\n",
    "Hint: The posterior (after the first cookie) becomes the prior (before the second cookie)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bowl 1 0.428571428571\n",
      "Bowl 2 0.571428571429\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "cookie['Bowl 1'] *= 0.25\n",
    "cookie['Bowl 2'] *= 0.5\n",
    "cookie.Normalize()\n",
    "cookie.Print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4:** Instead of doing two updates, what if we collapse the two pieces of data into one update?\n",
    "\n",
    "Re-initialize `Pmf` with two equally likely hypotheses and perform one update based on two pieces of data, a vanilla cookie and a chocolate cookie.\n",
    "\n",
    "The result should be the same regardless of how many updates you do (or the order of updates)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bowl 1 0.428571428571\n",
      "Bowl 2 0.571428571429\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "cookie = Pmf(['Bowl 1', 'Bowl 2'])\n",
    "cookie['Bowl 1'] *= 0.75 * 0.25\n",
    "cookie['Bowl 2'] *= 0.5 * 0.5\n",
    "cookie.Normalize()\n",
    "cookie.Print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dice problem\n",
    "---\n",
    "Create a Suite to represent dice with different numbers of sides."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 0.25\n",
      "6 0.25\n",
      "8 0.25\n",
      "12 0.25\n"
     ]
    }
   ],
   "source": [
    "suite = Suite([4, 6, 8, 12])\n",
    "suite.Print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 5:** We'll solve this problem two ways.  First we'll do it \"by hand\", as we did with the cookie problem; that is, we'll multiply each hypothesis by the likelihood of the data, and the renormalize.\n",
    "\n",
    "In the space below, update `suite` based on the likelihood of the data (rolling a 6), then normalize and print the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 0.0\n",
      "6 0.444444444444\n",
      "8 0.333333333333\n",
      "12 0.222222222222\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "suite[4] *= 0\n",
    "suite[6] *= 1/6\n",
    "suite[8] *= 1/8\n",
    "suite[12] *= 1/12\n",
    "\n",
    "suite.Normalize()\n",
    "suite.Print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 6:**  Now let's do the same calculation using `Suite.Update`.\n",
    "\n",
    "Write a definition for a new class called `Dice` that extends `Suite`.  Then define a method called `Likelihood` that takes `data` and `hypo` and returns the probability of the data (the outcome of rolling the die) for a given hypothesis (number of sides on the die).\n",
    "\n",
    "Hint: What should you do if the outcome exceeds the hypothetical number of sides on the die?\n",
    "\n",
    "Here's an outline to get you started:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Dice(Suite):\n",
    "        # hypo is the number of sides on the die\n",
    "        # data is the outcome\n",
    "        def Likelihood(self, data, hypo):\n",
    "            return 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "    \n",
    "class Dice(Suite):\n",
    "    # hypo is the number of sides on the die\n",
    "    # data is the outcome\n",
    "    def Likelihood(self, data, hypo):\n",
    "        if data > hypo:\n",
    "            return 0\n",
    "        else:\n",
    "            return 1 / hypo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can create a `Dice` object and update it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 0.0\n",
      "6 0.444444444444\n",
      "8 0.333333333333\n",
      "12 0.222222222222\n"
     ]
    }
   ],
   "source": [
    "dice = Dice([4, 6, 8, 12])\n",
    "dice.Update(6)\n",
    "dice.Print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we get more data, we can perform more updates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for roll in [8, 7, 7, 5, 4]:\n",
    "    dice.Update(roll)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 0.0\n",
      "6 0.0\n",
      "8 0.919293820933\n",
      "12 0.0807061790668\n"
     ]
    }
   ],
   "source": [
    "dice.Print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The German tank problem\n",
    "---\n",
    "The German tank problem is actually identical to the dice problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Tank(Suite):\n",
    "    # hypo is the number of tanks\n",
    "    # data is an observed serial number\n",
    "    def Likelihood(self, data, hypo):\n",
    "        if data > hypo:\n",
    "            return 0\n",
    "        else:\n",
    "            return 1 / hypo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the posterior probabilities after seeing Tank #37."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "62.822944785168964"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAEACAYAAABYq7oeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRKSc/w8yJrOJbfgUyQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8106adaa90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tank = Tank(range(100))\n",
    "tank.Update(37)\n",
    "thinkplot.Pdf(tank)\n",
    "tank.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 7:**  Suppose we see another tank with serial number 17.  What effect does this have on the posterior probabilities?\n",
    "\n",
    "Update the suite again with the new data and plot the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "57.81472076260485"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAEACAYAAABYq7oeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8106bdc810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "thinkplot.Pdf(tank, color='0.7')\n",
    "tank.Update(17)\n",
    "thinkplot.Pdf(tank)\n",
    "tank.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Euro problem\n",
    "---\n",
    "\n",
    "**Exercise 8:**  Write a class definition for `Euro`, which extends `Suite` and defines a likelihood function that computes the probability of the data (heads or tails) for a given value of `x` (the probability of heads).\n",
    "\n",
    "Note that `hypo` is in the range 0 to 100.  Here's an outline to get you started."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Euro(Suite):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\" \n",
    "        hypo is the prob of heads (0-100)\n",
    "        data is a string, either 'H' or 'T'\n",
    "        \"\"\"\n",
    "        return 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "class Euro(Suite):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\" \n",
    "        hypo is the prob of heads (0-100)\n",
    "        data is a string, either 'H' or 'T'\n",
    "        \"\"\"\n",
    "        x = hypo / 100\n",
    "        if data == 'H':\n",
    "            return x\n",
    "        else:\n",
    "            return 1-x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll start with a uniform distribution from 0 to 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAEACAYAAABPiSrXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUjNDQ5LUzNCQJDUzNCRJzf4foOWcrSf0qpcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8106f6e6d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro = Euro(range(101))\n",
    "thinkplot.Pdf(euro)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can update with a single heads:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAEACAYAAABYq7oeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nERG5ispBRESuonIQEZGrqBxEROQq/x/8+g7JrjO2aAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8106921450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro.Update('H')\n",
    "thinkplot.Pdf(euro)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another heads:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAEACAYAAABYq7oeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/H/cYFpqrQd1cQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f810695a450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro.Update('H')\n",
    "thinkplot.Pdf(euro)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And a tails:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAEACAYAAABYq7oeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n81hyMMYYcx5LDsYYY87z/wE3Qcameo1YXAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8106772050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro.Update('T')\n",
    "thinkplot.Pdf(euro)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Starting over, here's what it looks like after 7 heads and 3 tails."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "70"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAEACAYAAABYq7oeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nA6VVsMR4XJ9KAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f81069c5610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro = Euro(range(101))\n",
    "\n",
    "for outcome in 'HHHHHHHTTT':\n",
    "    euro.Update(outcome)\n",
    "\n",
    "thinkplot.Pdf(euro)\n",
    "euro.MaximumLikelihood()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The maximum posterior probability is 70%, which is the observed proportion.\n",
    "\n",
    "Here are the posterior probabilities after 140 heads and 110 tails."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEACAYAAABVtcpZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f81066a6850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro = Euro(range(101))\n",
    "\n",
    "evidence = 'H' * 140 + 'T' * 110\n",
    "for outcome in evidence:\n",
    "    euro.Update(outcome)\n",
    "    \n",
    "thinkplot.Pdf(euro)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior mean s about 56%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "55.952380952380956"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "euro.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So is the value with maximum posterior probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "56"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "euro.MaximumLikelihood()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior credible interval has a 90% chance of containing the true value (provided that the prior distribution truly represents our background knowledge)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(51, 61)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "euro.CredibleInterval(90)"
   ]
  },
  {
   "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",
    "To compute prior probabilities for values of λ, we'll use a Gamma distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def EvalGammaPdf(lam, a):\n",
    "    \"\"\"Computes the Gamma PDF.\n",
    "\n",
    "    lam: where to evaluate the PDF\n",
    "    a: parameter of the gamma distribution\n",
    "\n",
    "    returns: float probability\n",
    "    \"\"\"\n",
    "    return lam**(a-1) * math.exp(-lam) / gamma(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`MakeGammaPmf` takes a list of hypothetical rates and returns a Pmf object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def MakeGammaPmf(lams, a):\n",
    "    \"\"\"Makes a PMF discrete approx to a Gamma distribution.\n",
    "\n",
    "    lam: parameter lambda in events per unit time\n",
    "    xs: upper bound of the Pmf\n",
    "\n",
    "    returns: normalized Pmf\n",
    "    \"\"\"\n",
    "    pmf = Pmf()\n",
    "    for lam in lams:\n",
    "        pmf[lam] = EvalGammaPdf(lam, a)\n",
    "        \n",
    "    pmf.Normalize()\n",
    "    return pmf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the prior looks like.  I chose the parameter to yield a mean close to 1.3, which is the average number of goals per team per game in World Cup play."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3103599490022571"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEPCAYAAABMTw/iAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8106638b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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 9:**  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": 41,
   "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": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "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",
    "        x = data / 90\n",
    "        lam = hypo\n",
    "        like = lam * math.exp(-lam * x)\n",
    "        return like"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can create a `Soccer` object and initialize it with the prior Pmf:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3103599490022564"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEPCAYAAABMTw/iAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f81066478d0>"
      ]
     },
     "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": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0352677560937336"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEPCAYAAABMTw/iAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nme02YiV7SQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f810665b210>"
      ]
     },
     "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": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6029902257702706"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEPCAYAAACk43iMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYYRJEgghhBEmSSCEEEaYvwFqUFPTHwzKIwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8106fddf10>"
      ]
     },
     "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",
    "### Predictive distributions\n",
    "\n",
    "Now to predict the number of goals in the remaining 67 minutes.\n",
    "\n",
    "The distribution of additional goals (after the first two) is Poisson, with a parameter that is the product of `lam` and the remaining time (in games)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def EvalPoissonPmf(k, lam):\n",
    "    \"\"\"Computes the Poisson PMF.\n",
    "\n",
    "    k: number of events\n",
    "    lam: parameter lambda in events per unit time\n",
    "\n",
    "    returns: float probability\n",
    "    \"\"\"\n",
    "    return lam ** k * math.exp(-lam) / gamma(k+1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`MakePoissonPmf` makes a Pmf that represents a Poisson distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def MakePoissonPmf(lam, high, step=1):\n",
    "    \"\"\"Makes a PMF discrete approx to a Poisson distribution.\n",
    "\n",
    "    lam: parameter lambda in events per unit time\n",
    "    high: upper bound of the Pmf\n",
    "\n",
    "    returns: normalized Pmf\n",
    "    \"\"\"\n",
    "    pmf = Pmf()\n",
    "    for k in range(0, high + 1, step):\n",
    "        p = EvalPoissonPmf(k, lam)\n",
    "        pmf[k] = p\n",
    "    pmf.Normalize()\n",
    "    return pmf"
   ]
  },
  {
   "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": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEZCAYAAABsPmXUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8106cc9890>"
      ]
     },
     "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": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9377241975748247"
      ]
     },
     "execution_count": 49,
     "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": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.047208117119541926"
      ]
     },
     "execution_count": 50,
     "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": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEPCAYAAAC5sYRSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f810680ca50>"
      ]
     },
     "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": 52,
   "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": 53,
   "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": 54,
   "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": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEZCAYAAABsPmXUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAGF1JREFUeJzt3Xu4XXV95/H3JyCiQBhQjBogRmDQOANIn0YUcY5QELEV\nmHoBFUTbyHQMXqiW6sCDmeKIl3YsjVQygtaCYEUp+IiIQE+VQUwQBB1DwQFiCMhFUwSsTky+88de\niZvDOTn7JPvc1nm/nmc/WZffb63fSuCzf/u3bqkqJEntMmuyGyBJ6j/DXZJayHCXpBYy3CWphQx3\nSWohw12SWshwl4ZIskeSXyTJZLdF2lKGu6a9JCcluS3J40nuS3Jukp3HUP/uJIdunK+q1VU1u/p8\nE0iS3ZJ8IcmaJGuTfDvJwn7uQ9rIcNe0luRPgY8AfwrMBg4C5gHfTLLtZLZtGDsCy4EXA7sCnwe+\nluTpk9oqtVK8Q1XTVZKdgPuAk6rqy13LdwDuBv6sqj6X5EzgPwDrgaOAO4C3VdUPknweeDPwq2b9\nfwe+1NTftqo2JHkO8Gng5cDPgI9V1WeafZ0JLGjqHwusAt5aVTf3eAyPAANVdcvW/W1IT2TPXdPZ\ny4CnApd1L6yqx4ErgcO7Fr8W+CKwC3AxcHmSbarqROAnwO83QzGf2LiZrrpfbMo8G3g98D+SDHSt\n/wPgC8DOwFeBT/XS+CQHAE8BftxLeWksDHdNZ88EHq6qDcOsu79Zv9H3quqyqloP/BWwPZ0hnI2G\nPXmaZA/gpcBpVbWuqm4FPgOc2FXs+qr6RjNG//fAfqM1PMlsOsMyH6qqR0crL42V4a7p7GHgmUmG\n++/4Oc36jVZvnGhC+F7guT3s4znAz6vql13LVgFzu+Z/2jX9S2D7EdoEQJLtgSuAG6rqYz20QRoz\nw13T2XeAXwP/uXthkh2BVwPXdC3eo2t9gN2BNc2izZ14ug/YtRnH32jPrrpjkmQ74B+Bn1TVf9mS\nbUi9MNw1bVXVL+icAP2bJK9Ksm2S5/HbMfILu4r/TpJjkmwDvJfOCdDvNut+Cjx/yObT7ONe4Abg\nI0memmQ/4I/oDL+MZKQhnm2BL9Pp3Z/U42FKW8Rw17RWVR8HPgh8AniETm9+FfB7VbWuq+jlwBuB\ntXSujjm2GX8HOBs4I8nPk5y6cdNddY8H5tPpxX8ZOKOq/mlzzRph+cvoXK1zBPBIkkebm6UO7u1o\npd71dClkkiOBT9L5Mji/qj46ZP1rgb8ANgDrgPdW1f/upa403prLFfdqroyRZoRRe+7NiaGlwKuA\nFwHHJ3nBkGLXVNX+VfViOj9ZPzOGupKkPutlWGYhcGdVrWp+5l4CHN1dYMiVBDvS6cH3VFeS1H+9\n3J49l67LyOhcQvak52EkOYbObeC7Aa8ZS11pPFXVkslugzTR+nZCtar+sapeCBwDnNWv7UqSxq6X\nnvsaOtf1btR9ffCTVNX1SZ6fZNex1E3iQ24kaYyqathLb3vpua8A9k4yr7kB4zg6d9dtkmSvrukD\nge2q6ue91B3SyC36nHnmmVtcd7p+POb2f2ba8XrMY/9szqg996pan2QxcDW/vZxxZZKTO6trGfCH\nSU4E/h/wb8AbNld3tH1KkrZOT8+7rqqrgH2HLDuva/pjwLDPyBiuriRpfLXiDtWBgYHJbsKE85jb\nb6YdL3jM/TRlXtaRpKZKWyRpOkhCjXBCdaq9hkySnuB5z3seq1atmuxmTKp58+Zxzz33jKmOPXdJ\nU1rTO53sZkyqkf4ONtdzb8WYuyTpiQx3SWohw12SWshwl6Rxtnr1ambPnj2h5w48oSppShvuZOLi\nsy4e130uPf34cd3+WHlCVZIEGO6StMXmz5/PJz7xCfbff3922mknFi1axIMPPshRRx3F7NmzOeKI\nI3jkkUdYtWoVs2bNYsOGDaxdu5Y99tiDr33tawA8/vjj7LPPPlx44YWj7G1sDHdJ2gpf+cpXuPba\na7njjju44oorOOqoozj77LN5+OGHWb9+Peeccw7QGUIB2GWXXbjgggtYtGgRDz30EO95z3s48MAD\nectb3tLXdnmHqiRthVNOOYVnPvOZABxyyCHMmTOH/fbbD4Bjjz2W6667jhNPfOK72Q8//HBe//rX\nc9hhh7F27Vpuu+22vrfLnrskbYU5c+Zsmn7a0572pPnHHnts2HqLFi3ihz/8ISeddBK77LJL39tl\nuEvSBNuwYQPveMc7eOtb38q5557LXXfd1fd9GO6SNAG6L2X88Ic/zKxZs7jgggt43/vexwknnND3\na+Adc5c07UyV69A3niQdaX64dTfffDOf/OQnuemmm0jCaaedxpVXXsnZZ5/NBz7wgf61barcOORN\nTJKG41MhvYlJktQw3CWphQx3SWohT6g2xvtBRN2myskgSe1lz12SWshwl6QWclhG0pQ2b968zV4/\nPhPMmzdvzHUMd0lT2j333DPZTZiWHJaRpBYy3CWphXoK9yRHJrk9yR1JThtm/ZuS3Np8rk+yX9e6\ne5rltyRZ3s/GS5KGN+qYe5JZwFLgMOA+YEWSy6vq9q5idwGvqKpHkhwJLAMOatZtAAaqam1/my5J\nGkkvPfeFwJ1Vtaqq1gGXAEd3F6iqG6vqkWb2RmBu1+r0uB9JUp/0ErpzgdVd8/fyxPAe6o+Br3fN\nF/DNJCuSLBp7EyVJY9XXSyGTvBJ4G/DyrsUHV9X9SXajE/Irq+r6fu5XkvREvYT7GmDPrvndm2VP\n0JxEXQYc2T2+XlX3N38+lOQyOsM8w4b7hz70oU3TAwMDDAwM9NA8SZoZBgcHGRwc7KnsqC/rSLIN\n8C90TqjeDywHjq+qlV1l9gSuBU6oqhu7lj8dmFVVjyXZAbgaWFJVVw+zn0l9WYcPDpM03WzuZR2j\n9tyran2SxXSCeRZwflWtTHJyZ3UtA84AdgXOTec+4XVVtRCYA1yWpJp9XTRcsEuS+qunMfequgrY\nd8iy87qmFwFPOllaVXcDB2xlGyVJY+QlipLUQoa7JLWQ4S5JLWS4S1ILGe6S1EKGuyS1kOEuSS1k\nuEtSCxnuktRChrsktZDhLkktZLhLUgsZ7pLUQoa7JLWQ4S5JLWS4S1ILGe6S1EKGuyS1kOEuSS1k\nuEtSCxnuktRC2052A7otPuviCdvX0tOPn7B9SdJEs+cuSS1kuEtSC02pYZmZyKEoSePBnrsktZDh\nLkktZLhLUgsZ7pLUQj2Fe5Ijk9ye5I4kpw2z/k1Jbm0+1yfZr9e6kqT+GzXck8wClgKvAl4EHJ/k\nBUOK3QW8oqr2B84Clo2hriSpz3rpuS8E7qyqVVW1DrgEOLq7QFXdWFWPNLM3AnN7rStJ6r9ewn0u\nsLpr/l5+G97D+WPg61tYV5LUB329iSnJK4G3AS/fkvrLr7t00/Tc+QuYO39Bn1omSdPf4OAgg4OD\nPZXtJdzXAHt2ze/eLHuC5iTqMuDIqlo7lrobLTz0dT00R5JmpoGBAQYGBjbNL1myZMSyvQzLrAD2\nTjIvyXbAccAV3QWS7Al8GTihqv7vWOpKkvpv1J57Va1Pshi4ms6XwflVtTLJyZ3VtQw4A9gVODdJ\ngHVVtXCkuuN2NJIkoMcx96q6Cth3yLLzuqYXAYt6rStJGl/eoSpJLWS4S1ILGe6S1EKGuyS1kOEu\nSS1kuEtSCxnuktRChrsktZDhLkktZLhLUgsZ7pLUQoa7JLWQ4S5JLWS4S1ILGe6S1EKGuyS1kOEu\nSS1kuEtSCxnuktRChrsktZDhLkktZLhLUgsZ7pLUQoa7JLWQ4S5JLWS4S1ILGe6S1EKGuyS1UE/h\nnuTIJLcnuSPJacOs3zfJDUl+leTUIevuSXJrkluSLO9XwyVJI9t2tAJJZgFLgcOA+4AVSS6vqtu7\niv0MOAU4ZphNbAAGqmptH9orSepBLz33hcCdVbWqqtYBlwBHdxeoqoer6nvAb4apnx73I0nqk15C\ndy6wumv+3mZZrwr4ZpIVSRaNpXGSpC0z6rBMHxxcVfcn2Y1OyK+squuHK7j8uks3Tc+dv4C58xdM\nQPMkaXoYHBxkcHCwp7K9hPsaYM+u+d2bZT2pqvubPx9KchmdYZ5hw33hoa/rdbOSNOMMDAwwMDCw\naX7JkiUjlu1lWGYFsHeSeUm2A44DrthM+WyaSJ6eZMdmegfgCOCHPexTkrQVRu25V9X6JIuBq+l8\nGZxfVSuTnNxZXcuSzAFuAnYCNiR5N7AA2A24LEk1+7qoqq4er4ORJHX0NOZeVVcB+w5Zdl7X9APA\nHsNUfQw4YGsaKEkaOy9RlKQWMtwlqYUMd0lqoYm4zl1T0OKzLp7Q/S09/fgJ3Z8009lzl6QWMtwl\nqYUMd0lqIcNdklrIcJekFjLcJamFDHdJaiHDXZJayHCXpBYy3CWphQx3SWohw12SWshwl6QWMtwl\nqYUMd0lqIcNdklrIcJekFjLcJamFDHdJaiHDXZJayHCXpBYy3CWphQx3SWohw12SWqincE9yZJLb\nk9yR5LRh1u+b5IYkv0py6ljqSpL6b9RwTzILWAq8CngRcHySFwwp9jPgFODjW1BXktRnvfTcFwJ3\nVtWqqloHXAIc3V2gqh6uqu8BvxlrXUlS//US7nOB1V3z9zbLerE1dSVJW2jbyW5At+XXXbppeu78\nBcydv2ASWyNJU8vg4CCDg4M9le0l3NcAe3bN794s68WY6i489HU9blaSZp6BgQEGBgY2zS9ZsmTE\nsr0My6wA9k4yL8l2wHHAFZspn62oK0nqg1F77lW1Psli4Go6XwbnV9XKJCd3VteyJHOAm4CdgA1J\n3g0sqKrHhqs7bkcjSQJ6HHOvqquAfYcsO69r+gFgj17rSpLGl3eoSlILGe6S1EKGuyS1kOEuSS1k\nuEtSCxnuktRChrsktZDhLkktZLhLUgtNqadCamZYfNbFE7avpacfP2H7kqYSe+6S1EKGuyS1kOEu\nSS1kuEtSCxnuktRChrsktZDhLkktZLhLUgsZ7pLUQoa7JLWQ4S5JLWS4S1ILGe6S1EKGuyS1kOEu\nSS1kuEtSCxnuktRChrsktVBP4Z7kyCS3J7kjyWkjlDknyZ1Jvp/kxV3L70lya5JbkizvV8MlSSMb\n9R2qSWYBS4HDgPuAFUkur6rbu8q8GtirqvZJ8hLgb4GDmtUbgIGqWtv31kuShtVLz30hcGdVraqq\ndcAlwNFDyhwNfB6gqr4L7JxkTrMuPe5HktQnvYTuXGB11/y9zbLNlVnTVaaAbyZZkWTRljZUktS7\nUYdl+uDgqro/yW50Qn5lVV0/AfuVpBmrl3BfA+zZNb97s2xomT2GK1NV9zd/PpTkMjrDPMOG+/Lr\nLt00PXf+AubOX9BD8yRpZhgcHGRwcLCnsr2E+wpg7yTzgPuB44Djh5S5Angn8MUkBwH/WlUPJHk6\nMKuqHkuyA3AEsGSkHS089HU9NVqSZqKBgQEGBgY2zS9ZMmKcjh7uVbU+yWLgajpj9OdX1cokJ3dW\n17KqujLJUUl+DDwOvK2pPge4LEk1+7qoqq7ewuOSJPWopzH3qroK2HfIsvOGzC8ept7dwAFb00BJ\n0thNxAlVaUpYfNbFE7q/pacPHb2UJo7Xn0tSCxnuktRChrsktZDhLkktZLhLUgsZ7pLUQoa7JLWQ\n4S5JLWS4S1ILGe6S1EKGuyS1kOEuSS1kuEtSCxnuktRChrsktZDPc5cmwEQ+S97nyAvsuUtSKxnu\nktRChrsktZDhLkktZLhLUgsZ7pLUQoa7JLWQ4S5JLeRNTFKLTeTNU+ANVFOJPXdJaiHDXZJaqKdw\nT3JkktuT3JHktBHKnJPkziTfT3LAWOpKkvpr1DH3JLOApcBhwH3AiiSXV9XtXWVeDexVVfskeQnw\naeCgXur2w5q7f8Tc+Qv6uckpz2Nuv+l+vFsy3r+lxzydx/oHBwcZGBjo+3Z76bkvBO6sqlVVtQ64\nBDh6SJmjgc8DVNV3gZ2TzOmx7lZbc/eP+r3JKc9jbr+ZdrwwM495cHBwXLbby9Uyc4HVXfP30gnt\n0crM7bGuJPWNj1fuGK9LITNO25WkKWlLv1SWf+sHPLwFdUf7YklVbb5AchDwoao6spn/c6Cq6qNd\nZT4N/FNVfbGZvx34T8D80ep2bWPzDZEkPUlVDduZ7qXnvgLYO8k84H7gOGDoV8YVwDuBLzZfBv9a\nVQ8kebiHupttoCRp7EYN96pan2QxcDWdE7DnV9XKJCd3VteyqroyyVFJfgw8Drxtc3XH7WgkSUAP\nwzKSpOlnWt+hOtNukEqye5LrkvyfJD9I8q7JbtNESTIryc1JrpjstkyEJDsn+VKSlc2/90smu03j\nLcl7k/wwyW1JLkqy3WS3qd+SnJ/kgSS3dS3bJcnVSf4lyTeS7NyPfU3bcO+6QepVwIuA45O8YHJb\nNe5+A5xaVS8CXgq8cwYc80bvBmbSRdB/DVxZVS8E9gdaPZyZ5LnAKcCBVbUfnSHj4ya3VePis3Qy\nq9ufA9dU1b7AdcAH+rGjaRvuTNANUlNJVf20qr7fTD9G53/4uZPbqvGXZHfgKOAzk92WiZBkNnBI\nVX0WoKp+U1W/mORmTYRtgB2SbAs8nc5d7a1SVdcDa4csPhr4u2b674Bj+rGv6RzuI904NSMkeR5w\nAPDdyW3JhPifwPuBmXKCaD7wcJLPNkNRy5I8bbIbNZ6q6j7gL4GfAGvoXHF3zeS2asI8q6oegE4H\nDnhWPzY6ncN9xkqyI3Ap8O6mB99aSV4DPND8Ygkz4wa5bYEDgU9V1YHAL+n8dG+tJP+OTg92HvBc\nYMckb5rcVk2avnRipnO4rwH27JrfvVnWas1P1kuBv6+qyye7PRPgYOC1Se4CLgZemeTzk9ym8XYv\nsLqqbmrmL6UT9m32e8BdVfXzqloPfAV42SS3aaI80DyLiyTPBh7sx0anc7hvurmqOat+HJ2bqdru\nAuBHVfXXk92QiVBVH6yqPavq+XT+ja+rqhMnu13jqfmJvjrJv28WHUb7Tyb/hM6TZLdPEjrH3NaT\nyEN/gV4BnNRMvxXoS6dt2r5mbybeIJXkYODNwA+S3ELn59sHq+qqyW2ZxsG7gIuSPAW4i+bGwLaq\nquVJLgVuAdY1fy6b3Fb1X5IvAAPAM5L8BDgTOBv4UpK3A6uAN/RlX97EJEntM52HZSRJIzDcJamF\nDHdJaiHDXZJayHCXpBYy3CWphQx3TSlJ1jfPU7ml+fPPJmCfOyf5ky2od2aSU8ejTV37eHQ8t6/2\nmrY3Mam1Hm+epzKRdgH+K/C3E7zfXngjiraIPXdNNU96MFiS2c1LWfZp5r+Q5I+a6UeT/FXzkodv\nJnlGs/z5Sb6eZEWSf954K3+SZyX5SpLvN78ODgI+AuzV/FL4aFPufUmWN+XO7GrLf2teqvAtYN9h\nD6Cz7+8kuTXJX3T3vpN8vHnRyq1J3tAs2yHJNUluapa/dphtPrs5jpubl1kcvMV/w5oZqsqPnynz\nofNCkpvp3H5+M/D6ZvlhwA3AG+m8xGJj+Q3Acc30GcA5zfQ1wF7N9ELg2mb6EuBdzXSAneg8ifC2\nrm0eDpzXVearwMvpPLzrVuCpTb076bw8ZegxfBV4QzN9MvCLZvoPgW8008+ic6v5HDrPMd+xWf4M\nOu8p2LitjXVPBT7Q1aYdJvvfys/U/jgso6nmlzXMsExVXdv0dD8F/MeuVeuBf2imLwS+nGQHOk8U\n/FLzECqApzR/Hgqc0GyzgEeT7Dpkd0cAhye5mSZIgX2A2cBlVfVr4NebeeXfS/nti2O+AHy8mT6Y\nzpMtqaoHkwwCvwtcBZyd5BA6X1bPTfKsqup+OuAK4PzmWTOXV9WtI+xbAhxz1zTRhPQLgcfp9G7v\nH6Fo0RluXDvclwS9jWEH+EhV/a8hbXh3j83t3sfmnj+/cd2b6RzTi6tqQ5K7ge2fsMGqbyd5BfAa\n4HNJ/rKqLuyxPZqBHHPXVDNSGJ5K57G3bwI+m2SbZvk2wOua6TcD11fVo8DdSTYuJ8l+zeS1dE6e\nbnzp9mzgUTrDLBt9A3h78wuAJM9NshvwLeCYJE9NshPwByO09cauNnW/B/TbwBub/e4GHAIsB3YG\nHmyC/ZV0home8PeRZM+mzPl0XjfY9ue7ayvZc9dUs33XcEjRGbL4HPB24Her6pdJ/hk4HVhCpye/\nMMkZwAN0xuShE/SfTnI6nf/OLwFuA94DLGtOyP4G+JOq+m6SG9J5I/3Xq+q0JC8EvtOM6jwKvKWq\nbknyD812HqATzMN5L3Bhkg/S+aJ4BKCqLmtO4N5KZ/jl/c3wzEXAV5PcCtzEE59jvvFXwADw/iTr\nmva0+pn22no+8lfTWpJHq2qn0UtOnCRPq6p/a6bfSOeE77GT3CzNMPbcNd1Nxd7J7yRZSufXx1o6\nvzqkCWXPXZJayBOqktRChrsktZDhLkktZLhLUgsZ7pLUQoa7JLXQ/wdYjAQjXmT/owAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8106b5e690>"
      ]
     },
     "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 10:** Compute the predictive mean and the probability of scoring 5 or more additional goals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.9377505061485503, 0.085650136218385256)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "mix.Mean(), mix.ProbGreater(4)"
   ]
  }
 ],
 "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
}