{
 "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": 15,
   "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": 16,
   "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": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JbAX+fT+20SxJkyXVSqqtr69vfYCZme2XYgPg15J+I+lSSZcCvyI7eZ1LRGyLiD0R8Q5w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\nt/8PTX/Oa/NbjBsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe8daba8>"
      ]
     },
     "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": 21,
   "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": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bmtqN+5vb/80RURsRtf369TuYUs3MrAWthceIiLg4In4MnA+cdjAvls5hNPgHoOEE/AJg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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf44d198>"
      ]
     },
     "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": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pmf({1: 0.2, 2: 0.4, 3: 0.2, 5: 0.2})"
      ]
     },
     "execution_count": 24,
     "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": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4"
      ]
     },
     "execution_count": 25,
     "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": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4"
      ]
     },
     "execution_count": 26,
     "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": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6000000000000001"
      ]
     },
     "execution_count": 27,
     "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": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.30000000000000004"
      ]
     },
     "execution_count": 28,
     "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": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8999999999999999"
      ]
     },
     "execution_count": 29,
     "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": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 30,
     "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": 31,
   "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": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QtF7W9WHrh/Bg8PCRJKllKEiSWoaCJKllKEiSWoaCJKllKEiSWl6SKmmz4qWzozMUpE2U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\ngiSpZShIklqGgiSp9f8BXaPHLDF9vPkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e1ac18>"
      ]
     },
     "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": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZxqFgZmYZP3nNzGrq3kc2cMeqdj9Gs59yKJhZTZULhN6ex9yT0kdzDhvaTNusQreP8bTe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\nxqFgZmYZh4KZmWUcCmZmlnEomJlZ5v8Dws/0addRzZ0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe71e898>"
      ]
     },
     "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": 35,
   "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": 36,
   "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": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MPK1pnm8CZ2XmDdXra4H3ZebiTdZ1CnBK9XIv4J5h3noq8EjbPkj7WV8Z6ytj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\nqYCBWpIkSSpgoJYkSZIK/H/FQM3eee3+QQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf506ac8>"
      ]
     },
     "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": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xc13c0b8>"
      ]
     },
     "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": 40,
   "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": 41,
   "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": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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N7AHA0l43cPcfRVaZiIgkSnOBcVva64ooCxERkWQ7ZGC4+6OZKkRERJLtkIFhZod84JG7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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe427320>"
      ]
     },
     "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": 43,
   "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": 44,
   "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": 45,
   "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": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hSSpiYEiSihgYkqQiBoYkqYiBIUkqYmBIkooYGJKkIgaGJKmIgSFJKmJgSJKKGBiSpCIG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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe427080>"
      ]
     },
     "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": 47,
   "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>1.748448</td>\n",
       "      <td>-1.705241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.366154</td>\n",
       "      <td>0.341385</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.516255</td>\n",
       "      <td>1.719845</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.224272</td>\n",
       "      <td>0.982769</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1\n",
       "0  1.748448 -1.705241\n",
       "1 -0.366154  0.341385\n",
       "2 -0.516255  1.719845\n",
       "3  1.224272  0.982769"
      ]
     },
     "execution_count": 47,
     "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": 48,
   "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>1.748448</td>\n",
       "      <td>-1.705241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.366154</td>\n",
       "      <td>0.341385</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.516255</td>\n",
       "      <td>1.719845</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.224272</td>\n",
       "      <td>0.982769</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B\n",
       "0  1.748448 -1.705241\n",
       "1 -0.366154  0.341385\n",
       "2 -0.516255  1.719845\n",
       "3  1.224272  0.982769"
      ]
     },
     "execution_count": 48,
     "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": 49,
   "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>1.748448</td>\n",
       "      <td>-1.705241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>-0.366154</td>\n",
       "      <td>0.341385</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>-0.516255</td>\n",
       "      <td>1.719845</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>d</th>\n",
       "      <td>1.224272</td>\n",
       "      <td>0.982769</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B\n",
       "a  1.748448 -1.705241\n",
       "b -0.366154  0.341385\n",
       "c -0.516255  1.719845\n",
       "d  1.224272  0.982769"
      ]
     },
     "execution_count": 49,
     "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": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a    1.748448\n",
       "b   -0.366154\n",
       "c   -0.516255\n",
       "d    1.224272\n",
       "Name: A, dtype: float64"
      ]
     },
     "execution_count": 51,
     "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": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A    1.748448\n",
       "B   -1.705241\n",
       "Name: a, dtype: float64"
      ]
     },
     "execution_count": 53,
     "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": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A    1.748448\n",
       "B   -1.705241\n",
       "Name: a, dtype: float64"
      ]
     },
     "execution_count": 54,
     "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": 55,
   "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>1.748448</td>\n",
       "      <td>-1.705241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>-0.516255</td>\n",
       "      <td>1.719845</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B\n",
       "a  1.748448 -1.705241\n",
       "c -0.516255  1.719845"
      ]
     },
     "execution_count": 55,
     "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": 56,
   "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>1.748448</td>\n",
       "      <td>-1.705241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>-0.366154</td>\n",
       "      <td>0.341385</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>-0.516255</td>\n",
       "      <td>1.719845</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B\n",
       "a  1.748448 -1.705241\n",
       "b -0.366154  0.341385\n",
       "c -0.516255  1.719845"
      ]
     },
     "execution_count": 56,
     "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": 57,
   "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>1.748448</td>\n",
       "      <td>-1.705241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>-0.366154</td>\n",
       "      <td>0.341385</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B\n",
       "a  1.748448 -1.705241\n",
       "b -0.366154  0.341385"
      ]
     },
     "execution_count": 57,
     "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": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "resp = nsfg.ReadFemResp()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here\n",
    "pmf = thinkstats2.Pmf(resp.numkdhh, label='actual')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "actual\n"
     ]
    },
    {
     "data": {
      "image/png": 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7ImJ5tX81sJFWIOwC/hf4lbrqkSR1VusTzZm5kdYP/vZtq9uWE/j1OmuQJJ28rhholiRN\nDkNBklQYCpKkwlCQJBWGgiSpqO05hbpExF7gu03X0cEc4Nmmi5ggvXIuvXIe4LmcjrrhPF6bmR2f\n/u26UOgGETF8Mg+JdINeOZdeOQ/wXE5HvXIeYPeRJKmNoSBJKgyFeqxpuoAJ1Cvn0ivnAZ7L6ahX\nzsMxBUnSD3ilIEkqDIUJFBGLI+LJiNgVEbc0Xc9YRcS6iHgmIv6t6VrGKyIuiogHI2JnROyIiJVN\n1zRWETErIr4WEY9V5/KHTdc0HhExLSL+NSL+qelaxiMivhMR34iIRyOi6+f1t/togkTENFrvj7iK\n1mtFtwHvz8ydjRY2BhFxJbCf1vuzf6Lpesajeuf3BZn59Yg4B9gOXNel/y8BnJWZ+yOiD/gXYGX1\nfvOuExG/DQwC52bmNU3XM1YR8R1gMDNP9+cUTopXChPncmBXZj6VmQeBu4Ghhmsak8zcDDzXdB0T\nITP/IzO/Xi3/N/BNuvQ94Nmyv1rtq/505W91ETEXeBfwqaZr0dEMhYlzIbC7bX2ELv3h06siYgD4\nKeCrzVYydlWXy6PAM8CXMrNbz+XjwO8CR5ouZAIkcH9EbI+IZU0XM16GgqaEiDgb+ALwW5n5QtP1\njFVmvpyZC2m9z/zyiOi67r2IuAZ4JjO3N13LBHlb9X+yBPj1qvu1axkKE2cPcFHb+txqmxpW9b9/\nAfhsZv590/VMhMz8L+BBYHHTtYzBW4Frq774u4FFEfGZZksau8zcU/39DLCeVldy1zIUJs424JKI\nmBcRM4AbgQ0N1zTlVYOza4FvZuZfNF3PeEREf0T8ULX8Klo3NTzRbFWnLjN/PzPnZuYAre+TBzLz\ngw2XNSYRcVZ1AwMRcRbwc0BX37VnKEyQzDwMrADuozWY+fnM3NFsVWMTEZ8DtgCvj4iRiPhw0zWN\nw1uBD9H6bfTR6s/VTRc1RhcAD0bE47R+CflSZnb17Zw94IeBf4mIx4CvAV/MzHsbrmlcvCVVklR4\npSBJKgwFSVJhKEiSCkNBklQYCpKkwlBQT4qIP46Id0TEdRHx+6f4tf0R8dVqBs+fOYn2vxwRf3WC\nfRvbni3Yf4I2d0bEDadSo1QXQ0G96s3AVuBngc2n+LXvBL6RmT+VmQ+Pp4jMvLp6+viUVTPvSpPK\nUFBPiYg/qx7uuozWA3gfAT4ZEX9wnLYDEfFARDweEV+OiIsjYiHwp8BQ9aDbq475mssi4pHqnQZf\ne+VpVuBHIuLeiPh2RPxpW/vvRMScY44REfFX1bs37gdec0z72yLi68AvRMSPVcfdHhEPR8T8qt2d\nEbGqquUprzQ0UaY3XYA0kTLzdyLi88AvAr8NPJSZbz1B89uBT2fmpyPiV4FVmXldFSCDmbmivXE1\nfck9wNLM3BYR5wIvVrsX0pqB9SXgyYi4PTPbZ81t9x7g9cCltJ6I3Qmsa9u/LzPfVH3ml4Hlmfnt\niHgz8AlgUdXuAuBtwHxaU6r8Xcd/IKkDQ0G96E3AY7R+WH5zlHZvAd5bLf8NrSuE0bwe+I/M3Abw\nymyrremV+HJmfr9a3wm8lqOnUm93JfC5zHwZ+PeIeOCY/fdUxzkb+Gngb6vPAJjZ1u4fMvMIsDMi\nfrhD7dJJMRTUM6qunztpzVD7LHBma3M8CrwlM18c5cvH66W25ZcZ3/fW/1R/nwH8VzUtc6fPjBO0\nkU6JYwrqGZn5aPUD9Fu0umYeAH4+MxeeIBAeoTVLJ8BNQKdB5SeBCyLiMoCIOCcixvLDfzOwtHph\nzgXAO47XqLoSeToifqH6vIiIBWP4POmkGQrqKRHRDzxfdavM7/Au5t8AfqUamP4QsHK0Y1evWV0K\n3F7NivklYNYYylwPfJvWWMJdtAbET+Qm4MPV5+2gS1/xqu7hLKmSpMIrBUlSYShIkgpDQZJUGAqS\npMJQkCQVhoIkqTAUJEmFoSBJKv4PDqp9uRFMqIkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf828e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution goes here\n",
    "print('actual')\n",
    "thinkplot.pmf(pmf)\n",
    "thinkplot.Config(xlabel='# of children', ylabel='PMF')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here\n",
    "# biased numbers\n",
    "biased = BiasPmf(pmf, label='Biased')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Y/pLKHD6SJDUYQ0GSVDAUJEkFQ0GSVDAUJEkFQ0GSVDAUJEkFQ0GSVDAUJEkFQ0GSVDAU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\nEhMO70RVqAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe810198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution goes here\n",
    "thinkplot.PrePlot(2)\n",
    "thinkplot.Pmfs([pmf, biased])\n",
    "thinkplot.Config(xlabel='number of children', ylabel='pmf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0242051550438309"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution goes here\n",
    "# mean of pmf\n",
    "pmf.Mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.4036791006642821"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution goes here\n",
    "# biased mean\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": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "live, firsts, others = first.MakeFrames()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "preg_map = nsfg.MakePregMap(live)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here\n",
    "hist = thinkstats2.Hist()\n",
    "\n",
    "for i,j in preg_map.items():\n",
    "#     print('i=',i,'j=',j)\n",
    "    if len(j) >= 2:\n",
    "        pair = (preg.loc[j[0:2]].prglngth)\n",
    "        diff = np.diff(pair)[0]\n",
    "        hist[diff] += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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A7q2qz7Xyc0lWtOUrgJOtfhxYPbT6qlZ7haraXlXTVTU9NTU1TouSpHMY5+qgAJ8Cnqyq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\ngCR1zBCQpI79f+2whzYgO6PHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf62a8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution goes here\n",
    "thinkplot.Hist(hist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "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": 101,
   "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": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Y97KxelTJ/5el6lRaDr2nvyr5c14uiPR23r7IKpOQdYZCudVuM/hi6VPA7Ij4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf62afd0>"
      ]
     },
     "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": 110,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xe87def0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution goes here\n",
    "def Observed_Pmf(pmf, speed, label=None):\n",
    "    mod = pmf.Copy(label=label)\n",
    "    for i in mod.Values():\n",
    "#         print('values=',i)\n",
    "        diff = abs(i -speed)\n",
    "        mod[i] *= diff\n",
    "    mod.Normalize()\n",
    "    return mod\n",
    "        \n",
    "newpmf = Observed_Pmf(pmf, 7, label='observed')\n",
    "thinkplot.Pmf(newpmf)\n",
    "thinkplot.Config(xlabel='speed',ylabel='pmf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "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": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}