{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Examples and Exercises from Think Stats, 2nd Edition\n",
    "\n",
    "http://thinkstats2.com\n",
    "\n",
    "Copyright 2016 Allen B. Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "import nsfg\n",
    "import first\n",
    "import thinkstats2\n",
    "import thinkplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, I'll load the NSFG pregnancy file and select live births:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "preg = nsfg.ReadFemPreg()\n",
    "live = preg[preg.outcome == 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the histogram of birth weights:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/+2y7EBF++FFxD5IbX71AMtbTn0nGC4JkJNrF6fQ4kvGh+qfPRwGzM+sYB7xO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\nuThAzMwsl/8P4EXto8B89nQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15a86f3d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist = thinkstats2.Hist(live.birthwgt_lb, label='birthwgt_lb')\n",
    "thinkplot.Hist(hist)\n",
    "thinkplot.Config(xlabel='Birth weight (pounds)', ylabel='Count')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To normalize the disrtibution, we could divide through by the total count:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = hist.Total()\n",
    "pmf = hist.Copy()\n",
    "for x, freq in hist.Items():\n",
    "    hist[x] = freq / n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is a Probability Mass Function (PMF)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZdS9tBUinDjFiZmY9R1sH0YdJ+hGgzHSTiLiiYpWZmVlVaytArs5M/66ShZiZWffSaoBE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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f159a1dce90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Hist(pmf)\n",
    "thinkplot.Config(xlabel='Birth weight (pounds)', ylabel='PMF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "More directly, we can create a Pmf object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pmf({1: 0.2, 2: 0.4, 3: 0.2, 5: 0.2})"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pmf = thinkstats2.Pmf([1, 2, 2, 3, 5])\n",
    "pmf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Pmf` provides `Prob`, which looks up a value and returns its probability:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pmf.Prob(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The bracket operator does the same thing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pmf[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `Incr` method adds to the probability associated with a given values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6000000000000001"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pmf.Incr(2, 0.2)\n",
    "pmf[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `Mult` method multiplies the probability associated with a value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.30000000000000004"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pmf.Mult(2, 0.5)\n",
    "pmf[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Total` returns the total probability (which is no longer 1, because we changed one of the probabilities)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8999999999999999"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pmf.Total()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Normalize` divides through by the total probability, making it 1 again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pmf.Normalize()\n",
    "pmf.Total()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the PMF of pregnancy length for live births."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pmf = thinkstats2.Pmf(live.prglngth, label='prglngth')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what it looks like plotted with `Hist`, which makes a bar graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1599b4fed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Hist(pmf)\n",
    "thinkplot.Config(xlabel='Pregnancy length (weeks)', ylabel='Pmf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what it looks like plotted with `Pmf`, which makes a step function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZmeU4GMzMLMfBYGZmOQ4GMzPLcTCYmVmOg8HMzHIcDGZmluNgMDOzHAeDmZnlOBjMzCzH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\nmeU4GMzMLMfBYGZmOf8f0H1DdonF+u4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15cf477890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Pmf(pmf)\n",
    "thinkplot.Config(xlabel='Pregnancy length (weeks)', ylabel='Pmf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use `MakeFrames` to return DataFrames for all live births, first babies, and others."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "live, firsts, others = first.MakeFrames()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the distributions of pregnancy length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "first_pmf = thinkstats2.Pmf(firsts.prglngth, label='firsts')\n",
    "other_pmf = thinkstats2.Pmf(others.prglngth, label='others')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's the code that replicates one of the figures in the chapter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pDDNrdvcH2+9s5syZbcsNDQ1qaGjId70AkBeNjY1qbGwsdhmZomcDqEihPdvcPbYizKxa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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1599b45190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "width=0.45\n",
    "axis = [27, 46, 0, 0.6]\n",
    "thinkplot.PrePlot(2, cols=2)\n",
    "thinkplot.Hist(first_pmf, align='right', width=width)\n",
    "thinkplot.Hist(other_pmf, align='left', width=width)\n",
    "thinkplot.Config(xlabel='Pregnancy length(weeks)', ylabel='PMF', axis=axis)\n",
    "\n",
    "thinkplot.PrePlot(2)\n",
    "thinkplot.SubPlot(2)\n",
    "thinkplot.Pmfs([first_pmf, other_pmf])\n",
    "thinkplot.Config(xlabel='Pregnancy length(weeks)', axis=axis)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the code that generates a plot of the difference in probability (in percentage points) between first babies and others, for each week of pregnancy (showing only pregnancies considered \"full term\"). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/downey/anaconda2/lib/python2.7/site-packages/matplotlib/axes/_axes.py:519: UserWarning: No labelled objects found. Use label='...' kwarg on individual plots.\n",
      "  warnings.warn(\"No labelled objects found. \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1598633a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "weeks = range(35, 46)\n",
    "diffs = []\n",
    "for week in weeks:\n",
    "    p1 = first_pmf.Prob(week)\n",
    "    p2 = other_pmf.Prob(week)\n",
    "    diff = 100 * (p1 - p2)\n",
    "    diffs.append(diff)\n",
    "\n",
    "thinkplot.Bar(weeks, diffs)\n",
    "thinkplot.Config(xlabel='Pregnancy length(weeks)', ylabel='Difference (percentage points)')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Biasing and unbiasing PMFs\n",
    "\n",
    "Here's the example in the book showing operations we can perform with `Pmf` objects.\n",
    "\n",
    "Suppose we have the following distribution of class sizes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "d = { 7: 8, 12: 8, 17: 14, 22: 4, \n",
    "     27: 6, 32: 12, 37: 8, 42: 3, 47: 2 }\n",
    "\n",
    "pmf = thinkstats2.Pmf(d, label='actual')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function computes the biased PMF we would get if we surveyed students and asked about the size of the classes they are in."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def BiasPmf(pmf, label):\n",
    "    new_pmf = pmf.Copy(label=label)\n",
    "\n",
    "    for x, p in pmf.Items():\n",
    "        new_pmf.Mult(x, x)\n",
    "        \n",
    "    new_pmf.Normalize()\n",
    "    return new_pmf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following graph shows the difference between the actual and observed distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2cZchkrGi7pIaAKxy93XuXgU8CYxKnsHdt7r7a8Deepa3FNQoTZQOYVEjnWoRyTRRd0l1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\nUWCIiEgoCgwREQlFgSEiIqH8f0aws8y0JPQzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15986b0e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "biased_pmf = BiasPmf(pmf, label='observed')\n",
    "thinkplot.PrePlot(2)\n",
    "thinkplot.Pmfs([pmf, biased_pmf])\n",
    "thinkplot.Config(xlabel='Class size', ylabel='PMF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The observed mean is substantially higher than the actual."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual mean 23.6923076923\n",
      "Observed mean 29.1233766234\n"
     ]
    }
   ],
   "source": [
    "print('Actual mean', pmf.Mean())\n",
    "print('Observed mean', biased_pmf.Mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we were only able to collect the biased sample, we could \"unbias\" it by applying the inverse operation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def UnbiasPmf(pmf, label=None):\n",
    "    new_pmf = pmf.Copy(label=label)\n",
    "\n",
    "    for x, p in pmf.Items():\n",
    "        new_pmf[x] *= 1/x\n",
    "        \n",
    "    new_pmf.Normalize()\n",
    "    return new_pmf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can unbias the biased PMF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Unbiased mean 23.6923076923\n"
     ]
    }
   ],
   "source": [
    "unbiased = UnbiasPmf(biased_pmf, label='unbiased')\n",
    "print('Unbiased mean', unbiased.Mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And plot the two distributions to confirm they are the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1598627250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.PrePlot(2)\n",
    "thinkplot.Pmfs([pmf, unbiased])\n",
    "thinkplot.Config(xlabel='Class size', ylabel='PMF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pandas indexing\n",
    "\n",
    "Here's an example of a small DataFrame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.395483</td>\n",
       "      <td>0.636168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.302488</td>\n",
       "      <td>1.540846</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.849977</td>\n",
       "      <td>0.360978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.186987</td>\n",
       "      <td>-0.782963</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1\n",
       "0 -0.395483  0.636168\n",
       "1 -0.302488  1.540846\n",
       "2  0.849977  0.360978\n",
       "3 -1.186987 -0.782963"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas\n",
    "array = np.random.randn(4, 2)\n",
    "df = pandas.DataFrame(array)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can specify column names when we create the DataFrame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.395483</td>\n",
       "      <td>0.636168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.302488</td>\n",
       "      <td>1.540846</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.849977</td>\n",
       "      <td>0.360978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.186987</td>\n",
       "      <td>-0.782963</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B\n",
       "0 -0.395483  0.636168\n",
       "1 -0.302488  1.540846\n",
       "2  0.849977  0.360978\n",
       "3 -1.186987 -0.782963"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "columns = ['A', 'B']\n",
    "df = pandas.DataFrame(array, columns=columns)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also specify an index that contains labels for the rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>-0.395483</td>\n",
       "      <td>0.636168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>-0.302488</td>\n",
       "      <td>1.540846</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>0.849977</td>\n",
       "      <td>0.360978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>d</th>\n",
       "      <td>-1.186987</td>\n",
       "      <td>-0.782963</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B\n",
       "a -0.395483  0.636168\n",
       "b -0.302488  1.540846\n",
       "c  0.849977  0.360978\n",
       "d -1.186987 -0.782963"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index = ['a', 'b', 'c', 'd']\n",
    "df = pandas.DataFrame(array, columns=columns, index=index)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normal indexing selects columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a   -0.395483\n",
       "b   -0.302488\n",
       "c    0.849977\n",
       "d   -1.186987\n",
       "Name: A, dtype: float64"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['A']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the `loc` attribute to select rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A   -0.395483\n",
       "B    0.636168\n",
       "Name: a, dtype: float64"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.loc['a']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you don't want to use the row labels and prefer to access the rows using integer indices, you can use the `iloc` attribute:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A   -0.395483\n",
       "B    0.636168\n",
       "Name: a, dtype: float64"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.iloc[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`loc` can also take a list of labels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>-0.395483</td>\n",
       "      <td>0.636168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>0.849977</td>\n",
       "      <td>0.360978</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B\n",
       "a -0.395483  0.636168\n",
       "c  0.849977  0.360978"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indices = ['a', 'c']\n",
    "df.loc[indices]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you provide a slice of labels, `DataFrame` uses it to select rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>-0.395483</td>\n",
       "      <td>0.636168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>-0.302488</td>\n",
       "      <td>1.540846</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>0.849977</td>\n",
       "      <td>0.360978</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B\n",
       "a -0.395483  0.636168\n",
       "b -0.302488  1.540846\n",
       "c  0.849977  0.360978"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['a':'c']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you provide a slice of integers, `DataFrame` selects rows by integer index."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>-0.395483</td>\n",
       "      <td>0.636168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>-0.302488</td>\n",
       "      <td>1.540846</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B\n",
       "a -0.395483  0.636168\n",
       "b -0.302488  1.540846"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[0:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But notice that one method includes the last elements of the slice and one does not.\n",
    "\n",
    "In general, I recommend giving labels to the rows and names to the columns, and using them consistently."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Something like the class size paradox appears if you survey children and ask how many children are in their family. Families with many children are more likely to appear in your sample, and families with no children have no chance to be in the sample.\n",
    "\n",
    "Use the NSFG respondent variable `numkdhh` to construct the actual distribution for the number of children under 18 in the respondents' households.\n",
    "\n",
    "Now compute the biased distribution we would see if we surveyed the children and asked them how many children under 18 (including themselves) are in their household.\n",
    "\n",
    "Plot the actual and biased distributions, and compute their means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "resp = nsfg.ReadFemResp()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "pmf = thinkstats2.Pmf(resp.numkdhh, label='numkdhh')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BtJPmd0wfEYGg0c1uImknzZk5rWW7WFqxW0vl8MxAkmQYSJIMA0kShoEkCcNAkoRhIEnC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15984d6ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "thinkplot.Pmf(pmf)\n",
    "thinkplot.Config(xlabel='Number of children', ylabel='PMF')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "biased = BiasPmf(pmf, label='biased')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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a6yY6EvgpUAhsBP7V3Q+0R2EiItJ+GjvyXwgMA94BfgD8Y+gViYhIu2vsmsHp7n4mgJnN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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15982c3d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "thinkplot.PrePlot(2)\n",
    "thinkplot.Pmfs([pmf, biased])\n",
    "thinkplot.Config(xlabel='Number of children', ylabel='PMF')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0242051550438309"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "pmf.Mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.4036791006642821"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "biased.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "**Exercise:** I started this book with the question, \"Are first babies more likely to be late?\" To address it, I computed the difference in means between groups of babies, but I ignored the possibility that there might be a difference between first babies and others for the same woman.\n",
    "\n",
    "To address this version of the question, select respondents who have at least live births and compute pairwise differences. Does this formulation of the question yield a different result?\n",
    "\n",
    "Hint: use `nsfg.MakePregMap`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "live, firsts, others = first.MakeFrames()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "preg_map = nsfg.MakePregMap(live)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "hist = thinkstats2.Hist()\n",
    "\n",
    "for caseid, indices in preg_map.items():\n",
    "    if len(indices) >= 2:\n",
    "        pair = preg.loc[indices[0:2]].prglngth\n",
    "        diff = np.diff(pair)[0]\n",
    "        hist[diff] += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEACAYAAABVtcpZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nf6OQhW9pdqIzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f15895a0410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "thinkplot.Hist(hist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.05636743215031337"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "pmf = thinkstats2.Pmf(hist)\n",
    "pmf.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** In most foot races, everyone starts at the same time. If you are a fast runner, you usually pass a lot of people at the beginning of the race, but after a few miles everyone around you is going at the same speed.\n",
    "When I ran a long-distance (209 miles) relay race for the first time, I noticed an odd phenomenon: when I overtook another runner, I was usually much faster, and when another runner overtook me, he was usually much faster.\n",
    "\n",
    "At first I thought that the distribution of speeds might be bimodal; that is, there were many slow runners and many fast runners, but few at my speed.\n",
    "\n",
    "Then I realized that I was the victim of a bias similar to the effect of class size. The race was unusual in two ways: it used a staggered start, so teams started at different times; also, many teams included runners at different levels of ability.\n",
    "\n",
    "As a result, runners were spread out along the course with little relationship between speed and location. When I joined the race, the runners near me were (pretty much) a random sample of the runners in the race.\n",
    "\n",
    "So where does the bias come from? During my time on the course, the chance of overtaking a runner, or being overtaken, is proportional to the difference in our speeds. I am more likely to catch a slow runner, and more likely to be caught by a fast runner. But runners at the same speed are unlikely to see each other.\n",
    "\n",
    "Write a function called `ObservedPmf` that takes a `Pmf` representing the actual distribution of runners’ speeds, and the speed of a running observer, and returns a new `Pmf` representing the distribution of runners’ speeds as seen by the observer.\n",
    "\n",
    "To test your function, you can use `relay.py`, which reads the results from the James Joyce Ramble 10K in Dedham MA and converts the pace of each runner to mph.\n",
    "\n",
    "Compute the distribution of speeds you would observe if you ran a relay race at 7 mph with this group of runners."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import relay\n",
    "\n",
    "results = relay.ReadResults()\n",
    "speeds = relay.GetSpeeds(results)\n",
    "speeds = relay.BinData(speeds, 3, 12, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4uYiZtXAysQ4plEj8XMTMWriZyzrNXVDNLJ9rJmZmVjInEzMzK5mbuaxNXruk\n+zr9/AWtz7o8+aNlzTUTa5PXLum+0t83T/5oWXMysTYVWrvEuiePEbIsZd7MJWk88GNyiWtBRFxe\noMw8YALwJnBGRKxu61xJlwJf492137+bLMJlGWpZu8Rqk5cBtlJkWjORVAdcAxwPHAxMkfSRvDIT\ngJERsT8wHZjfwXPnRMSY5MuJxHqscjU9ehlgK0XWzVxjgbURsS4itgKLgca8Mo3AIoCIWAn0kTSo\nA+cq49jNqlI6eZSz6dHLAFspsm7mGgJsSG1vJJck2iszpAPnzpD0T8ADwHci4vVyBd3TeR6u6ubm\nRqtG1dg1uCM1jmuB70VESPoBMAco+Bs2a9as1tcNDQ00NDSUIcTa5nm4uq/de/d6T6cJfyiw9jQ1\nNdHU1FTSNbJOJpuA4antocm+/DLDCpTpXezciHgptf9G4JfFAkgnE+sYz8PVfZ024Yj3PERftPR3\nlQ7Lqlz+B+3Zs2d3+hpZJ5NVwChJI4A/A5OBKXlllgHnAEskjQNei4hmSS8XO1fS4IjYnJx/CvBY\nxvfRIxQaoOh5uLqXQuvKlCOZ5Dd9ureX5cv0AXxEbAdmAMuBx4HFEfGkpOmSzkrK3An8SdIzwPXA\nN9o6N7n0FZL+KGk18CngW1neR0/hAYrVpdD/f6W+J/k/G+7tZfkyf2aSdNs9MG/f9XnbMzp6brJ/\najljtBwPUKwu6SYrqOz3pNBzFz+LsbRqfABvVcA9hiovy6WQCw1QNCuFp1Mx64E8QNHKzcnErAfy\nAEUrNzdz9XAeoGhtmTRzvjtiWIe4ZtLDeYCitccfNKwjnEx6OA9QtEL8gcI6SxFR6RgyIylq+f46\nO2V4oYFn6WTiAYq1adLM+a2vOzq9SsvPQvrcQjx4sTZJIiI6NZmuaybdWGd75BQaeGY9Szm+5+la\ni3uCWQsnk26ssz1ynDwsbVebsk6bcMR7EoqZe3NlzHMaWTXqaDNWIS2DKXfl3HLz71f1cM0kY57T\nyCotvwZSSw/X/ftVPZxMMuY5jazS0s1StdZbz79f1cPNXGY1Lss5vsxaOJnUmJYRy243tq5UbOLI\nznRd76q4fnnPI/zljS30q9+Tn35/atHyUPwZzFcvWVT0Gj2Vm7lqkNuNraPKtWZKoW7q1TCZZKEY\n/vLGFoDWf4uVT5+Tr61r9FSZJxNJ4yWtkfS0pAuKlJknaa2k1ZIOa+9cSf0kLZf0lKRfSeqT9X1U\nu/w/AG7mytbTAAAI1klEQVQ3to7I7+a7q89UCnVTr4bJJMvRfd6/Sx2T6Qh4SXXA08CngRfILeM7\nOSLWpMpMAGZExAmSjgTmRsS4ts6VdDnwSkRckSSZfhFxYYH379IR8O2NME/b1Wp/+j1e2vg0/2vo\nAUDhrp6FmhvaUm0j4JuamnZal7qWdJd7K9T9tyPditM/m/l2792LPffoxZa3tr6nOQmKN411ZlLS\nlnPbW7I4/z2K3VP+78Y/Tvr2TvdXa03L1TgCfiywNiLWRcRWYDHQmFemEVgEEBErgT6SBrVzbiOw\nMHm9EDg529vomPZGmJdj5HD6PV7a+PR7rlvoPQotx9sduos2NTVVOoTMdJd7a+vnpK2fmZafzULe\nfmcrf3ljS8HmpLaaxtpKJPk/0x39/drV38P8+3PTcvbJZAiwIbW9MdnXkTJtnTsoIpoBImIzMLCM\nMe+y9j4xlWPkcHsTMxZ6j0LL8dZyd1Ern7Z+Tgo1kfWr37PdfcW01zTWXi1/V3+/ytWM1dObw6qx\nN1enqlaJbjGbY6GRw6WMIj5twhHMmrXz8rrtjU5OL8dbK1Vyy05b3YrbOjZr1gZmzXpvs+mu/Ly3\n1dRWKKZyvUdnjhsQEZl9AeOAu1PbFwIX5JWZD5yW2l4DDGrrXOBJcrUTgMHAk0XeP/zlL3/5y1+d\n/+rs3/usayargFGSRgB/BiYDU/LKLAPOAZZIGge8FhHNkl5u49xlwBnA5cA0YGmhN+/sAyQzM9s1\nmSaTiNguaQawnNzzmQUR8aSk6bnDcUNE3ClpoqRngDeBL7d1bnLpy4F/l/QVYB1wapb3YWZmbavp\nxbHMzKxr1OQIeElDJa2Q9LikRyWdV+mYyk1SnaSHJC2rdCzlJqmPpFslPZl8D4+sdEzlJOlbkh6T\n9EdJP5fUu9IxlULSAknNkv6Y2lczA4uL3N8Vyc/nakm3S6qvZIylKHR/qWPfkbRDUv/2rlOTyQTY\nBnw7Ig4GPg6cI+kjFY6p3GYCT1Q6iIzMBe6MiIOAQ8l1uKgJkj4EnAuMiYiPkmtqnlzZqEp2M3B8\n3r4Lgd9ExIHACuCiLo+qfArd33Lg4Ig4DFhL7d0fkoYCx5F7lNCumkwmEbE5IlYnr/9G7o9R/viW\nbiv5Jk8EflrpWMot+YT3DxFxM0BEbIuINyocVrntBnxA0vuAPcnN8NBtRcR/A3/J212VA4t3RaH7\ni4jfRMSOZPP3wNAuD6xMinz/AH4EnN/R69RkMkmTtC9wGLCyspGUVcs3uRYfeH0YeFnSzUkz3g2S\n3l/poMolIl4A/hVYD2wi13vxN5WNKhMDq3FgcUa+AtxV6SDKSdJJwIaIeLSj59R0MpG0F3AbMDOp\noXR7kk4AmpOal9i1QZ7V7H3AGOAnETEG2EKuyaQmSOpL7lP7COBDwF6STq9sVF2iFj/4IOliYGtE\n3FLpWMol+fD2XeDS9O72zqvZZJI0IdwG/FtEFByH0k19AjhJ0nPAL4CjJS2qcEzltJHcJ6KWiY5u\nI5dcasWxwHMR8WpEbAf+AziqwjFloTmZYw9Jg4EXKxxP2Uk6g1xzc619GBgJ7As8IulP5JrwHpTU\nZu2yZpMJcBPwRETMrXQg5RQR342I4RGxH7kHtysiomZW50maRjZIapmS9dPUVkeD9cA4SXtIErn7\nq4UOBvm15JaBxdDGwOJuZKf7kzSeXFPzSRHxdsWiKp/W+4uIxyJicETsFxEfJvcB7/CIaPMDQU0m\nE0mfAL4IHCPp4aTtfXyl47IOOw/4uaTV5Hpz/bDC8ZRNRPyBXG3rYeARcr/AN1Q0qBJJugX4H+AA\nSeslfRm4DDhO0lPkEuZllYyxFEXu72pgL+DXyd+XaysaZAmK3F9a0IFmLg9aNDOzktVkzcTMzLqW\nk4mZmZXMycTMzErmZGJmZiVzMjEzs5I5mZiZWcmcTKzHknRxMhX8I8lYgY9l/H73SCo4mj+Zcn/f\nMrzHCEkF51OSdKWko0t9D7NCsl6216wqJUtETwQOi4htyXoNFVlXRNJooC4ini/TJYsNHrsauBG4\np0zvY9bKNRPrqfYBXo6IbQDJXFmbAST9SdLlyeJVv5e0X7J/gKTbJK1Mvo5K9u+ZLDD0e0kPJjOu\nkkyZ8otkga//APYoEssXSU03IumvyeJLjyULTH0sqdU8I+mzSZlpku5I9j8l6X+nrve+ZLblxyTd\nLWn35B7XA/3bm2PJbFc4mVhPtRwYLmmNpJ9I+se8439JFq/6CbnFukj+nRMRRwKf5931ZC4G/m9E\njAOOAa5MZl79OvBmskjbpcARRWL5BPBgavsD5BaWOgT4G/B9clOSnJK8bvEx4HPkppz5QqoJbX/g\n6uT814FJqXMeTt7PrKzczGU9UkS8mfzx/QdyCWCxpAsjomUG5sXJv78A5iSvjwUOSiZohNz08XsC\nnwFOlNSykFBvYDjwjySJKCIelfRIkXD2AV5Kbb8dEcuT148Cb0XEjuRZyIhUuV9HxGsASc3nk+Rq\nOM+l1qF4kNwMsC1eJDf1vVlZOZlYjxW5ienuA+5L/lBPBVqSSfq5Q8vrOuDIiNiavk6SWyZFxNoC\n+3faVSSULezcBJa+/g7g7ZZ4k6UV8uPK307PYrs979p7AP+vSBxmu8zNXNYjSTpA0qjUrsPYea3r\n05J/JwO/S17/CpiZusahqf3npfYflry8j9zzECQdAny0SDhPAulY2pqhNX3sOEl9kya1k4H7O3D+\nAcBjbRw32yWumVhPtRdwtaQ+wDbgGeCs1PF+SbPUW8CUZN9M4CfJ/t3IJYtvAD8Afizpj+T+kP8J\nOAm4DrhZ0uPkEsYDFHYncDSwItluayrv9LE/kFtcawi5ReAekjSi2PlJrWZkG3GY7TJPQW+WJ1ld\n7u8j4tUuer89yCWST0QHfyElTSMX43ntFn73nJPJLXJ0abuFzTrJzVxm79Wln7Ai4i1yvb2GZPxW\nuwH/mvF7WA/lmomZmZXMNRMzMyuZk4mZmZXMycTMzErmZGJmZiVzMjEzs5I5mZiZWcn+P8LtI7y7\nwMf3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1599b06fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf = thinkstats2.Pmf(speeds, 'actual speeds')\n",
    "thinkplot.Pmf(pmf)\n",
    "thinkplot.Config(xlabel='Speed (mph)', ylabel='PMF')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "def ObservedPmf(pmf, speed, label=None):\n",
    "    \"\"\"Returns a new Pmf representing speeds observed at a given speed.\n",
    "\n",
    "    The chance of observing a runner is proportional to the difference\n",
    "    in speed.\n",
    "\n",
    "    Args:\n",
    "        pmf: distribution of actual speeds\n",
    "        speed: speed of the observing runner\n",
    "        label: string label for the new dist\n",
    "\n",
    "    Returns:\n",
    "        Pmf object\n",
    "    \"\"\"\n",
    "    new = pmf.Copy(label=label)\n",
    "    for val in new.Values():\n",
    "        diff = abs(val - speed)\n",
    "        new[val] *= diff\n",
    "    new.Normalize()\n",
    "    return new\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SrihS5hZJyyUtlnRUsq+vpMckPS3pOUnTUuWnSVot6ankZ1zW92FmZsVlOjRYUg/gVuAE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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1598533a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "biased = ObservedPmf(pmf, 7, label='observed speeds')\n",
    "thinkplot.Pmf(biased)\n",
    "thinkplot.Config(xlabel='Speed (mph)', ylabel='PMF')"
   ]
  },
  {
   "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
}