chap03ex.ipynb

{
 "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": {},
   "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": {},
   "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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111357910>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {},
   "outputs": [],
   "source": [
    "n = hist.Total()\n",
    "pmf = hist.Copy()\n",
    "for x, freq in hist.Items():\n",
    "    pmf[x] = freq / n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is a Probability Mass Function (PMF)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEKCAYAAAAB0GKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAHEpJREFUeJzt3X+YVmW97/H3p+GXIu4MJk3AQCOVVNg6AQaa1MELf+xwh6cNKWk7Li41tv2wtrjtst3JznafOntbGwzROOpV6FaTDin5I9ONHEkZi58iSkgwWDmiFGqig9/zx1pDj8PMPPcws+Z5dD6v65pr1rrXutd8Z2Dm89xrredeigjMzMzKeVelCzAzs7cHB4aZmSVxYJiZWRIHhpmZJXFgmJlZEgeGmZklcWCYmVmSQgND0mRJGyVtkjSnle1TJK2RtEpSvaQJJdu2SFrbvK3IOs3MrDwV9cY9STXA08AkoAFYCUyPiCdL9jkIeCUiQtIJwO0RcUy+bQtQFxEvFFKgmZl1SK8Cjz0G2BQRmwEk3QZMAfYGRkS8XLJ/f6BT6TVo0KAYNmxYZw5hZtajPPHEEy9ERG3KvkUGxmBgW8l6AzC25U6S/hb4F+C9wFklmwL4uaQ9wPURsaDcFxw2bBj19T57ZWaWStJvU/et+EXviFicn4Y6B/hmyaYJETEaOAP4vKRTW+svaVZ+/aO+sbGxGyo2M+uZigyM7cDQkvUheVurImIZcKSkQfn69vzz88BislNcrfVbEBF1EVFXW5s0qjIzs/1QZGCsBEZIGi6pDzANWFK6g6QPSFK+fCLQF9ghqb+kAXl7f+B0YF2BtZqZWRmFXcOIiCZJs4H7gBpgYUSsl3RRvn0+MBX4jKQ3gD8Df5ffMXUosDjPkl7Aooi4t6hazawy3njjDRoaGnjttdcqXco7Xr9+/RgyZAi9e/fe72MUdlttJdTV1YUvepu9fTz77LMMGDCAgQMHkr9AtAJEBDt27GDXrl0MHz78LdskPRERdSnHqfhFbzPruV577TWHRTeQxMCBAzs9knNgmFlFOSy6R1f8nB0YZmaWpMg37pmZdcjsq2/t0uPN/dr0Lj1eT+fAMGtHV/wB8x+t6rZlyxbOPvts1q176537M2fO5Mtf/jIjR47cp8+1117LrFmzOPDAAwE46KCDePnll/fZb3/t3LmTRYsWcckllyTVfdNNN1FfX8/cuXO7rIbW+JSUmVkrbrzxxlbDYs+ePVx77bW8+uqrhX3tnTt3ct111xV2/P3lwDCzHq+pqYnzzjuPY489lnPPPZdXX32V0047be/cdAcddBCXXXYZo0aN4lvf+hbPPfccEydOZOLEiXuPceWVVzJq1CjGjRvHH/7wB/bs2cPw4cOJCHbu3ElNTQ3Lli0D4NRTT+WZZ56hsbGRSZMm8aEPfYiZM2fy/ve/nxdeeIE5c+bwm9/8htGjR/PVr3416XvYtm0bp512GiNGjOAb3/hG1/+QcGCYmbFx40YuueQSNmzYwMEHH7zPq/tXXnmFsWPHsnr1aq666ioOP/xwHnroIR566KG928eNG8fq1as59dRTueGGG6ipqeHoo4/mySefZPny5Zx44ok88sgj7N69m23btu39w/6xj32M9evXc+6557J161YArrnmGo466ihWrVrFt7/97aTv4fHHH+fHP/4xa9as4Y477ihkIlYHhpn1eEOHDmX8+PEAnH/++Sxfvvwt22tqapg6dWqb/fv06cPZZ58NwEknncSWLVsAOOWUU1i2bBnLli3jiiuuYPny5axcuZIPf/jDACxfvpxp06YBMHnyZA455JD9/h4mTZrEwIEDOeCAA/jkJz+5z/fQFRwYZtbjtXyPQsv1fv36UVNT02b/3r177+1TU1NDU1MTkJ16euSRR3j88cc588wz2blzJw8//DCnnHJKF38H5b+HruC7pMysalTqjrKtW7eyYsUKTj75ZBYtWsSECRP46U9/2ub+AwYMYNeuXQwaNKjd444ZM4YZM2Zw5JFH0q9fP0aPHs3111/P3XffDcD48eO5/fbbufzyy7n//vt56aWX3nL8jnjggQd48cUXOeCAA/jJT37CwoULO9Q/hUcYZtbjHX300cybN49jjz2Wl156iYsvvrjd/WfNmsXkyZPfctG7NX379mXo0KGMGzcOyE5R7dq1i+OPPx6Ar3/969x///0cd9xx3HHHHRx22GF759YaP348xx13XPJF7zFjxjB16lROOOEEpk6dSl1d0vRQHeLJB83a4fdhFGvDhg0ce+yxlS6jYnbv3k1NTQ29evVixYoVXHzxxaxataqwr9faz7sjkw/6lJSZWYVs3bqVT33qU7z55pv06dOHG264odIltcuBYWZWISNGjODXv/51u/usXbuWGTNmvKWtb9++PPbYY0WW1ioHhplVVER4xtp2HH/88V1ymqorLj/4oreZVUy/fv3YsWNHl/wxs7Y1P0CpX79+nTqORxhmVjFDhgyhoaGBxsbGSpfyjtf8iNbOcGCYWcX07t17n0eGWvXyKSkzM0viwDAzsyQODDMzS1JoYEiaLGmjpE2S5rSyfYqkNZJWSaqXNCG1r5mZda/CAkNSDTAPOAMYCUyX1PLxVQ8CoyJiNPD3wI0d6GtmZt2oyBHGGGBTRGyOiNeB24AppTtExMvxlxuw+wOR2tfMzLpXkYExGNhWst6Qt72FpL+V9BRwD9koI7mvmZl1n4pf9I6IxRFxDHAO8M2O9pc0K7/+Ue83/5iZFafIwNgODC1ZH5K3tSoilgFHShrUkb4RsSAi6iKirra2tvNVm5lZq4oMjJXACEnDJfUBpgFLSneQ9AHls45JOhHoC+xI6WtmZt2rsKlBIqJJ0mzgPqAGWBgR6yVdlG+fD0wFPiPpDeDPwN/lF8Fb7VtUrWZmVl6hc0lFxFJgaYu2+SXL/wr8a2pfMzOrnIpf9DYzs7cHB4aZmSVxYJiZWRIHhpmZJXFgmJlZEgeGmZklcWCYmVkSB4aZmSVxYJiZWRIHhpmZJXFgmJlZEgeGmZklcWCYmVkSB4aZmSVxYJiZWRIHhpmZJXFgmJlZEgeGmZklcWCYmVkSB4aZmSVxYJiZWRIHhpmZJSk0MCRNlrRR0iZJc1rZfp6kNZLWSnpU0qiSbVvy9lWS6ous08zMyutV1IEl1QDzgElAA7BS0pKIeLJkt2eBj0bES5LOABYAY0u2T4yIF4qq0czM0hU5whgDbIqIzRHxOnAbMKV0h4h4NCJeyld/CQwpsB4zM+uEIgNjMLCtZL0hb2vL54CflawH8HNJT0iaVUB9ZmbWAYWdkuoISRPJAmNCSfOEiNgu6b3AA5KeiohlrfSdBcwCOOKII7qlXjOznqjIEcZ2YGjJ+pC87S0knQDcCEyJiB3N7RGxPf/8PLCY7BTXPiJiQUTURURdbW1tF5ZvZmaligyMlcAIScMl9QGmAUtKd5B0BHAXMCMini5p7y9pQPMycDqwrsBazcysjMJOSUVEk6TZwH1ADbAwItZLuijfPh+4ChgIXCcJoCki6oBDgcV5Wy9gUUTcW1St9s4y++pbO32MuV+b3gWVmL2zFHoNIyKWAktbtM0vWZ4JzGyl32ZgVMt2MzOrHL/T28zMkjgwzMwsiQPDzMySODDMzCyJA8PMzJI4MMzMLIkDw8zMkjgwzMwsiQPDzMySODDMzCyJA8PMzJI4MMzMLIkDw8zMkjgwzMwsiQPDzMySODDMzCyJA8PMzJI4MMzMLIkDw8zMkjgwzMwsiQPDzMyS9Kp0AWY9xeyrb+30MeZ+bXoXVGK2fwodYUiaLGmjpE2S5rSy/TxJayStlfSopFGpfc3MrHsVFhiSaoB5wBnASGC6pJEtdnsW+GhEHA98E1jQgb5mZtaNihxhjAE2RcTmiHgduA2YUrpDRDwaES/lq78EhqT2NTOz7lVkYAwGtpWsN+Rtbfkc8LOO9pU0S1K9pPrGxsZOlGtmZu2pirukJE0kC4zLO9o3IhZERF1E1NXW1nZ9cWZmBhR7l9R2YGjJ+pC87S0knQDcCJwRETs60tfMzLpPkSOMlcAIScMl9QGmAUtKd5B0BHAXMCMinu5IXzMz616FjTAioknSbOA+oAZYGBHrJV2Ub58PXAUMBK6TBNCUn15qtW9RtZqZWXmFvnEvIpYCS1u0zS9ZngnMTO1rZmaVUxUXvc3MrPo5MMzMLEm7gSHpppLlCwqvxszMqla5EcaokuUvFFmImZlVt3KBEd1ShZmZVb1yd0kNkfQ9QCXLe0XEpYVVZmZmVaVcYHy1ZLm+yELMzKy6tRsYEXFzdxViZmbVrd3AkNTudBwR8YmuLcfMzKpVuVNSJ5NNM34r8BjZtQwzM+uBygXGYcAkYDrwaeAe4FbP62Rm1vO0e1ttROyJiHsj4gJgHLAJeDifGNDMzHqQspMPSuoLnEU2yhgGfA9YXGxZZmZWbcpd9L4FOI5s1thvRMS6bqnKzMyqTrkRxvnAK2TTgnxBUvM7vwVERBxcZHFmZlY9yr0Pw7PZmpkZUP6UVD/gIuADwBqyJ981dUdhZmZWXcqNIG4G6oC1wJnA/y68IjMzq0rlrmGMjIjjAST9AHi8+JLMzKwalRthvNG84FNRZmY9W7kRxihJf8qXBRyQr/suKTOzHqbcXVI13VWImZlVt0Jvm5U0WdJGSZskzWll+zGSVkjaLekrLbZtkbRW0ipJfhaHmVmFlZ0aZH9JqgHmkU1e2ACslLQkIp4s2e1F4FLgnDYOMzEiXiiqRjMzS1fkCGMMsCkiNkfE68BtwJTSHSLi+YhYScnFdTMzq05FBsZgsmdpNGvI21IF8HNJT0ia1dZOkmZJqpdU39jYuJ+lmplZOdU89ceEiBgNnAF8XtKpre0UEQsioi4i6mpra7u3QjOzHqTIwNgODC1ZH5K3JYmI7fnn58mmUx/TpdWZmVmHFBkYK4ERkoZL6gNMA9p9RngzSf0lDWheBk4HPLW6mVkFFXaXVEQ05U/muw+oIZu4cL2ki/Lt8yUdBtQDBwNvSvoiMBIYBCyW1Fzjooi4t6hazcysvMICAyAilpI9fKm0bX7J8u/JTlW19CdgVJG1mZlZx1TzRW8zM6siDgwzM0viwDAzsyQODDMzS+LAMDOzJA4MMzNL4sAwM7MkDgwzM0viwDAzsyQODDMzS+LAMDOzJA4MMzNL4sAwM7MkDgwzM0viwDAzsyQODDMzS+LAMDOzJA4MMzNL4sAwM7MkDgwzM0viwDAzsySFBoakyZI2StokaU4r24+RtELSbklf6UhfMzPrXoUFhqQaYB5wBjASmC5pZIvdXgQuBb6zH33NzKwbFTnCGANsiojNEfE6cBswpXSHiHg+IlYCb3S0r5mZda8iA2MwsK1kvSFvK7qvmZkV4G1/0VvSLEn1kuobGxsrXY6Z2TtWkYGxHRhasj4kb+vSvhGxICLqIqKutrZ2vwo1M7PyigyMlcAIScMl9QGmAUu6oa+ZmRWgV1EHjogmSbOB+4AaYGFErJd0Ub59vqTDgHrgYOBNSV8ERkbEn1rrW1StZmZWXmGBARARS4GlLdrmlyz/nux0U1JfMzOrnLf9RW8zM+seDgwzM0viwDAzsyQODDMzS+LAMDOzJA4MMzNL4sAwM7MkDgwzM0viwDAzsySFvtPbLNXsq2/t9DHmfm16F1RiZm3xCMPMzJI4MMzMLIkDw8zMkjgwzMwsiS96m70N+SYBqwSPMMzMLIkDw8zMkjgwzMwsiQPDzMySODDMzCyJA8PMzJI4MMzMLEmhgSFpsqSNkjZJmtPKdkn6Xr59jaQTS7ZtkbRW0ipJ9UXWaWZm5RX2xj1JNcA8YBLQAKyUtCQinizZ7QxgRP4xFvh+/rnZxIh4oagazcwsXZEjjDHApojYHBGvA7cBU1rsMwW4JTK/BN4t6X0F1mRmZvupyMAYDGwrWW/I21L3CeDnkp6QNKuwKs3MLEk1zyU1ISK2S3ov8ICkpyJiWcud8jCZBXDEEUd0d41mZj1GkSOM7cDQkvUheVvSPhHR/Pl5YDHZKa59RMSCiKiLiLra2touKt3MzFoqMjBWAiMkDZfUB5gGLGmxzxLgM/ndUuOAP0bE7yT1lzQAQFJ/4HRgXYG1mplZGYWdkoqIJkmzgfuAGmBhRKyXdFG+fT6wFDgT2AS8Cnw2734osFhSc42LIuLeomo1M7PyCr2GERFLyUKhtG1+yXIAn2+l32ZgVJG1mZlZx/id3mZmlsSBYWZmSRwYZmaWxIFhZmZJHBhmZpbEgWFmZkkcGGZmlsSBYWZmSRwYZmaWxIFhZmZJqnl6c6tis6++tUuOM/dr07vkOGZWPI8wzMwsiQPDzMySODDMzCyJA8PMzJI4MMzMLIkDw8zMkvi2WrMeritukfbt0T2DRxhmZpbEI4wexK8kzawzPMIwM7MkDgwzM0tS6CkpSZOB7wI1wI0RcU2L7cq3nwm8ClwYEb9K6dtT+DSSmVWLwgJDUg0wD5gENAArJS2JiCdLdjsDGJF/jAW+D4xN7Fu1/EfezN6JihxhjAE2RcRmAEm3AVOA0j/6U4BbIiKAX0p6t6T3AcMS+ppZlfEsxu9sRQbGYGBbyXoD2Sii3D6DE/t2KY8KzKqPfy+ri7IX9wUcWDoXmBwRM/P1GcDYiJhdss/dwDURsTxffxC4nGyE0W7fkmPMAmblq0cDGwv5hmAQ8EJBx+6saq3NdXVctdbmujqmWuuCfWt7f0TUpnQscoSxHRhasj4kb0vZp3dCXwAiYgGwoLPFliOpPiLqiv46+6Naa3NdHVettbmujqnWuqBztRV5W+1KYISk4ZL6ANOAJS32WQJ8RplxwB8j4neJfc3MrBsVNsKIiCZJs4H7yG6NXRgR6yVdlG+fDywlu6V2E9lttZ9tr29RtZqZWXmFvg8jIpaShUJp2/yS5QA+n9q3wgo/7dUJ1Vqb6+q4aq3NdXVMtdYFnaitsIveZmb2zuKpQczMLIkDI4GkyZI2StokaU6l6wGQNFTSQ5KelLRe0hcqXVMpSTWSfp3fOl018jeH3inpKUkbJJ1c6ZoAJH0p/3dcJ+lWSf0qWMtCSc9LWlfS9h5JD0h6Jv98SJXU9e3833KNpMWS3l0NdZVsu0xSSBpULXVJ+of8Z7Ze0v/qyDEdGGWUTFNyBjASmC5pZGWrAqAJuCwiRgLjgM9XSV3NvgBsqHQRrfgucG9EHAOMogpqlDQYuBSoi4jjyG70mFbBkm4CJrdomwM8GBEjgAfz9e52E/vW9QBwXEScADwNXNHdRdF6XUgaCpwObO3ugnI30aIuSRPJZs0YFREfAr7TkQM6MMrbO8VJRLwONE9TUlER8bvmiRojYhfZH77Bla0qI2kIcBZwY6VrKSXpr4BTgR8ARMTrEbGzslXt1Qs4QFIv4EDguUoVEhHLgBdbNE8Bbs6XbwbO6daiaL2uiLg/Ipry1V+SvWer4nXl/h34R6AiF4rbqOtisjdL7873eb4jx3RglNfW9CVVQ9Iw4K+BxypbyV7Xkv2ivFnpQloYDjQC/yc/XXajpP6VLioitpO90tsK/I7s/Uj3V7aqfRyav0cK4PfAoZUspg1/D/ys0kUASJoCbI+I1ZWupYUPAqdIekzSf0n6cEc6OzDe5iQdBPwY+GJE/KkK6jkbeD4inqh0La3oBZwIfD8i/hp4hcqcWnmL/HrAFLJAOxzoL+n8ylbVtvx2+Kq6vVLSlWSnaX9UBbUcCPwTcFWla2lFL+A9ZKexvwrcnj9mIokDo7yUKU4qQlJvsrD4UUTcVel6cuOBT0jaQnb67mOSfljZkvZqABoionkkdidZgFTafwOejYjGiHgDuAv4SIVraukP+UzS5J87dCqjSJIuBM4GzovqeJ/AUWThvzr/PRgC/ErSYRWtKtMA3BWZx8nOAiRfkHdglFeV05Tkrwp+AGyIiH+rdD3NIuKKiBgSEcPIfla/iIiqeLUcEb8Htkk6Om/6ONUxZf5WYJykA/N/149TBRfjW1gCXJAvXwD83wrWspeyB639I/CJiHi10vUARMTaiHhvRAzLfw8agBPz/3+V9hNgIoCkDwJ96MAkiQ6MMvILas3TlGwAbq+SaUrGAzPIXsGvyj/OrHRRbwP/APxI0hpgNPA/K1wP+YjnTuBXwFqy38uKvVNY0q3ACuBoSQ2SPgdcA0yS9AzZiKjbn4DZRl1zgQHAA/nvwPx2D9J9dVVcG3UtBI7Mb7W9DbigI6Myv9PbzMySeIRhZmZJHBhmZpbEgWFmZkkcGGZmlsSBYWZmSRwYVnUk7clvkVwt6VeSPpK3Hy7pzjb6DJP06ZL1CyXNLbDGiyR9psw+bdYg6Z/a6SdJv5B0cGfr3B+S/lnSV9rZfrak/9GdNVl1cGBYNfpzRIyOiFFks4/+C0BEPBcR57bcOZ+wbxjw6ZbbihIR8yPilk4cos3AIHts8epqmOqlDfcAf5NPgWE9iAPDqt3BwEuwdxSxLl++UNISSb8gm277GrJJ1VZJ+lLe93BJ9+bPcNhn3n9JH5Z0V748RdKfJfWR1E/S5rz9qPwYT0h6RNIxefveV+H5cdbkX/vbLZ4/sE8Nkq4hm5l2laTW5j46j/yd1Pn3/JSkHyl7fsedzX+oJX08n0RxrbJnH/TN27cof/6CpDpJD5fUvFDSw5I2S7q05GdxpaSnJS0Hji5pv1TZM1fWSLoN9s4l9TDZdBzWk0SEP/xRVR/AHmAV8BTwR+CkvH0YsC5fvpBsyoX35OunAXeXHONCYDPwV0A/4LfA0BZfpxewOV/+Dtk0MOOBjwK35u0PAiPy5bFkU50A/DPwlXx5HXByvnxNixpbrQF4uZ3v/7fAgJLvOYDx+fpC4Cv58bYBH8zbbyGbgBJgCzAoX64DHi6p+VGgL9n8QTuA3sBJZO8wP5AsoDeVfG/PAX3z5XeX1Hge8B+V/r/ij+798AjDqlHzKaljyB4Ac0s+x1JLD0REa88haPZgRPwxIl4jmzPq/aUbI5v25TeSjiV77sm/kT0v4xTgEWUzAX8EuEPSKuB64H2lx1D2hLcBEbEib1rUkRra8J7InnHSbFtE/L98+YfABLJRwLMR8XTefnNeezn3RMTuiHiBbALBQ/Pvd3FEvBrZabDSudLWkE2lcj7ZbLDNniebWdd6kF6VLsCsPRGxIj+9UtvK5lfKdN9dsryH1v+/LyN7muIbwM/JnlJWQzb187uAnRExuoNld7SGlpokvSsimp8n0nL+nnLz+TTxl9PNLR/12tF6ziILor8BrpR0fB60/YA/l+lr7zAeYVhVy68Z1JCdPmnPLrJJ6DrqEeCLwIqIaAQGkr16X5e/2n5W0n/Pa5GkUaWdI3ti3y5JY/Om1EervqFsevrWbASOLFk/Qn959vingeX5PsMkfSBvnwH8V768hew0E8DUhFqWAedIOkDSALJwQNK7yE6hPQRcTnZq7aC8zwfJTsVZD+LAsGrUfEF4FfCfZDNq7inTZw2wJ78V90tl9i31GNlpmWUlx1kbEc2v4s8DPidpNbCe1h/P+znghrze/mTXXcpZAKxp46L3PWTXZJptJHtm+wbgELIHQL0GfJbsdNlasucaNM/U+g3gu5LqyUYR7YrsUb//Cawme2LdynxTDfDD/Pi/Br4Xf3mk7cS8TutBPFutWSdJOigiXs6X5wDvi4gvdOJ47wNuiYhJyh6/e3dEHNclxXYBSYcCiyLi45WuxbqXr2GYdd5Zkq4g+336LdndUfstIn4n6YZKvXEvwRHAZZUuwrqfRxhmZpbE1zDMzCyJA8PMzJI4MMzMLIkDw8zMkjgwzMwsiQPDzMyS/H+hh+LDC37mpgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a16869bd0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {},
   "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": {},
   "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": {},
   "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": {},
   "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": {},
   "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": {},
   "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": {},
   "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": {},
   "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": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a17901810>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a16a2f690>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {},
   "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": {},
   "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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a17823a10>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a178ae150>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {},
   "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": {},
   "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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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txJi7F8Z27pr27Wljxjc7d4ithmzUXGCcDFwEXAl8D/gT8Ed3Xx11YZmksPiqNnZMfjaQo9QuLycx/1f2u/Ph9t1xl5FVDnlbrbvvc/fn3P1aYBCwDngpePTqMSMp/wGSQp/c5GDGD+1Ju7ycuMtosN91538mNfuIVjNrB3yXVC+jCHgAKI+2rPjMmzY87hJidfsza+MuQRKsbFARZYOK4i6DEfctjbuErNTcRe/HgH6knst9l7u/lZGqREQkcZrrYVwNfEZqWpApZlbf/zPA3f34KIsTEZHkaO57GJrNVkREgOaHpPKBScB/AlYBs929LhOFiYhIsjTXg3gUKAXeBC4G/k/kFYmISCI1dw2jr7ufAWBms4DXoi9JRESSqLkeRm39Cw1FiYhkt+Z6GP3NbFfw2oD2wbLukhIRyTLN3SWVnK90iohIrHTbrIiIhKLAEBGRUJqdS0okmy17bxuL393K3jpNcicSaQ/DzEaa2Ttmts7Mpjax/XQzW25mX5jZrYdzrEgmJC0sTLOzSowiCwwzywEeBEYBfYErzaxvo922Az8C/uUIjhWJXNLCIq9Od7dLfKIckhoIrHP39QBmNgcoA96u38HdtwBbzOy7h3usSKb94tLTYzv3mLs/iO3cIvWiHJLqRurxrvWqgnVRHysiIhFo9XdJmdlEM6sws4rq6uq4yxEROWZFGRibgO5py4XBuhY91t1nunupu5cWFBQcUaEiItK8KANjJdDLzHqYWVtgAjA/A8eKiEgEIrvo7e51ZjYZeB7IIfUsjdVmNinYPsPMTgYqgOOB/Wb2Y1Iz5O5q6tioahURkeZF+sU9d19A6nng6etmpL3+iNRwU6hjRUQkPvqmt8ghfLRjNx9u381+d93aKlmv1d8lJRKl+rBIinZ5mkBa4qPAEDmEpIXF+KE94y5DspiGpERCmjdteNwliMRKPQwREQlFgSEiIqEoMEREJBQFhoiIhKKL3iLSqt3+zNrYzt0217iwd1eG9OwSWw2ZpB6GiLQ6SXny4N46Z/G7W+MuI2MUGCLS6uTV1SUqNLKFhqREpNVpW1dH2+BxtXE9CTHOobC4qIchIiKhKDBERCQUBYaIiISiwBARkVAUGCIiEooCQ0REQlFgiIhIKAoMEREJRYEhIiKhKDBERCQUBYaIiISiuaQSZNl721j87tasmsxMRFoPBUaCJCks2uZa3CU0GHP3wvhO3r59fOcWSRgFRoIkKSwu7N011hramLE/IdNXQ6oekYOJe+baTD3ISYGRUHFN2ZwU3+zcgQ+3705EaLQx45udO8RdhiRM21xLzIe8+gc5KTAkK518YgdOPjH1RzrO8Iz7k6Mk14W9uyZqGDkTdSgwJPH0R1uSaEjPLol4lncm/3/otlpJpCRddIfk1SMSBwWGJNKFvbsm5o90Em4CEEmCSIekzGwk8K9ADvCwu9/TaLsF2y8GdgPXuftfg20bgE+BfUCdu5dGWaskS1K6+yLypcgCw8xygAeBi4AqYKWZzXf3t9N2GwX0Cn7OAf4t+F3vfHffGlWNIiISXpRDUgOBde6+3t33AnOAskb7lAGPecoK4Gtm9o0IaxIRkSMUZWB0AzamLVcF68Lu48AiM6s0s4kHO4mZTTSzCjOrqK6uboGyRUSkKUm+6D3E3UtIDVv90MzObWond5/p7qXuXlpQUJDZCkVEskiUF703Ad3TlguDdaH2cff631vMrJzUENeSyKoVkVYpzrnG2uXlMH5oT8oGFcVWQyZF2cNYCfQysx5m1haYAMxvtM984PuWMgjY6e6bzayjmR0HYGYdgeHAWxHWKiKtSLu8nLhLAOCL2n08sfS9uMvImMgCw93rgMnA88AaYK67rzazSWY2KdhtAbAeWAf8O/DfgvVfB5aZ2RvAa8Cf3P25qGoVkdZl/NCeiQqNbBHp9zDcfQGpUEhfNyPttQM/bOK49UD/KGsTkdarbFBR7MNAsU67H5MkX/QWEZEEUWCIiEgoCgwREQlFgSEiIqHoeRjA3txcanNzcTM9e0FE5CDUw4CGsEiKpEzrLSKSToEBiQsLPXtBRJJIQ1KNxPn8aBGRJFMPQ0REQlEPQ0TkKMX5re+a9u1pY8Y3O3eI/FzqYYiIHIGkzGUFsN+dD7fvjvw8CgwRkSOQpAkQIRUaUdOQlIjIEUjCBIgAI+5bmrFzqYchIiKhKDBERCQUBYaIiISiwBARkVAUGCIiEooCQ0REQlFgiIhIKAoMEREJRYEhIiKhKDBERCQUBYaIiISiwBARkVAUGCIiEooCQ0REQlFgiIhIKAoMEREJRYEhIiKhRBoYZjbSzN4xs3VmNrWJ7WZmDwTbV5nZWWGPFRGRzIosMMwsB3gQGAX0Ba40s76NdhsF9Ap+JgL/dhjHiohIBkXZwxgIrHP39e6+F5gDlDXapwx4zFNWAF8zs2+EPFZERDIoysDoBmxMW64K1oXZJ8yxIiKSQa3+oreZTTSzCjOrqK6ujrscEZFjVpSBsQnonrZcGKwLs0+YYwFw95nuXurupQUFBUddtIiINC03wvdeCfQysx6k/thPAL7XaJ/5wGQzmwOcA+x0981mVh3i2Bbz/C1Do3prEZFIZfLvV2SB4e51ZjYZeB7IAWa7+2ozmxRsnwEsAC4G1gG7gR8c6tioahURkeaZu8ddQ4spLS31ioqKuMsQEWk1zKzS3UvD7NvqL3qLiEhmKDBERCQUBYaIiISiwBARkVAUGCIiEsoxdZdU8P2Nv8ddRwvqCmyNu4gEUXt8SW1xILXHgQ6nPf7B3UN96/mYCoxjjZlVhL3dLRuoPb6ktjiQ2uNAUbWHhqRERCQUBYaIiISiwEi2mXEXkDBqjy+pLQ6k9jhQJO2haxgiIhKKehgiIhKKAiMhzGy2mW0xs7fS1nU2sz+b2f8Lfp8YZ42ZYmbdzexFM3vbzFab2ZRgfba2R76ZvWZmbwTtcVewPivbA8DMcszsb2b2f4PlbG6LDWb2ppm9bmYVwbpI2kOBkRy/BUY2WjcVWOzuvYDFwXI2qAP+h7v3BQYBPzSzvmRve3wBXODu/YESYKSZDSJ72wNgCrAmbTmb2wLgfHcvSbuVNpL2UGAkhLsvAbY3Wl0GPBq8fhS4LKNFxcTdN7v7X4PXn5L6w9CN7G0Pd/eaYDEv+HGytD3MrBD4LvBw2uqsbItDiKQ9FBjJ9nV33xy8/gj4epzFxMHMioAzgVfJ4vYIhmBeB7YAf3b3bG6P+4H/CexPW5etbQGpDw+LzKzSzCYG6yJpjygf0SotyN3dzLLqljYz6wTMA37s7rvMrGFbtrWHu+8DSszsa0C5mfVrtD0r2sPMLgG2uHulmQ1rap9saYs0Q9x9k5mdBPzZzNamb2zJ9lAPI9k+NrNvAAS/t8RcT8aYWR6psPiDuz8VrM7a9qjn7p8AL5K63pWN7TEYGG1mG4A5wAVm9nuysy0AcPdNwe8tQDkwkIjaQ4GRbPOBa4PX1wJPx1hLxliqKzELWOPu96Ztytb2KAh6FphZe+AiYC1Z2B7u/o/uXujuRcAE4AV3v5osbAsAM+toZsfVvwaGA28RUXvoi3sJYWZ/BIaRmmXyY+B/A/8BzAVOITUL7zh3b3xh/JhjZkOApcCbfDlOPY3UdYxsbI9iUhcuc0h9yJvr7j8zsy5kYXvUC4akbnX3S7K1LczsVFK9CkhdYnjc3X8RVXsoMEREJBQNSYmISCgKDBERCUWBISIioSgwREQkFAWGiIiEosAQCZjZyWY2x8zeC6ZZWGBmvc2sKH0W4QzUUWpmD2TqfCJhaWoQERq+LFgOPOruE4J1/UnNwbMxk7W4ewVQkclzioShHoZIyvlArbvPqF/h7m+4+9L0nYLexlIz+2vw85+D9d8wsyXBMwneMrOhwYSBvw2W3zSzWxqf1Mz+S7D9DTNbEqwblvachwXBe75uZjvN7Nrgff/ZzFaa2Soz+6+RtoxIQD0MkZR+QGWI/bYAF7n7HjPrBfwRKAW+BzwffMs2B+hA6tkV3dy9H0D99B6N3AmMCCaP+8p2d784OPZs4BFS3/6/Adjp7gPMrB3wspktdPf3D/PfLHJYFBgihycP+LWZlQD7gN7B+pXA7GDSxP9w99fNbD1wqplNB/4ELGzi/V4Gfmtmc4GnmtiOmXUFfkdqeoedZjYcKDazscEuJwC9AAWGREpDUiIpq4GzQ+x3C6m5vvqT6lm0hYYHYJ0LbCIVAN939x3Bfi8BkzjwgT8Ex00C/hfQHagM5gBqEPRW5gA/c/f6C+8G/PfgCWsl7t7D3ZsKI5EWpcAQSXkBaJf2ABrMrNjMhjba7wRgs7vvB64hNSEgZvYPwMfu/u+kguGsoGfQxt3nkQqFsxqf1Mx6uvur7n4nUE0qONLdA6xy9zlp654Hbg56MwR3cnU84n+5SEgakhKh4SEzlwP3m9lPgD3ABuDHjXZ9CJhnZt8HngM+C9YPA24zs1qgBvg+qcfKPmJm9R/M/rGJU/9zcC3ESD17+Q3gvLTttwKrg6ftQeqax8NAEfDX4O6uavRIUskAzVYrIiKhaEhKRERCUWCIiEgoCgwREQlFgSEiIqEoMEREJBQFhoiIhKLAEBGRUBQYIiISyv8HL0MTePX6wlMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a17aa6850>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {},
   "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": {},
   "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": {},
   "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": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a19437ed0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\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>-0.015974</td>\n",
       "      <td>0.652920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.367530</td>\n",
       "      <td>0.852663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.215394</td>\n",
       "      <td>-0.352673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.269258</td>\n",
       "      <td>0.386105</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1\n",
       "0 -0.015974  0.652920\n",
       "1  0.367530  0.852663\n",
       "2 -0.215394 -0.352673\n",
       "3  2.269258  0.386105"
      ]
     },
     "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": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\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>-0.015974</td>\n",
       "      <td>0.652920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.367530</td>\n",
       "      <td>0.852663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.215394</td>\n",
       "      <td>-0.352673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.269258</td>\n",
       "      <td>0.386105</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B\n",
       "0 -0.015974  0.652920\n",
       "1  0.367530  0.852663\n",
       "2 -0.215394 -0.352673\n",
       "3  2.269258  0.386105"
      ]
     },
     "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": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\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>-0.015974</td>\n",
       "      <td>0.652920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>0.367530</td>\n",
       "      <td>0.852663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>-0.215394</td>\n",
       "      <td>-0.352673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>d</th>\n",
       "      <td>2.269258</td>\n",
       "      <td>0.386105</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B\n",
       "a -0.015974  0.652920\n",
       "b  0.367530  0.852663\n",
       "c -0.215394 -0.352673\n",
       "d  2.269258  0.386105"
      ]
     },
     "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": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a   -0.015974\n",
       "b    0.367530\n",
       "c   -0.215394\n",
       "d    2.269258\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": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A   -0.015974\n",
       "B    0.652920\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": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A   -0.015974\n",
       "B    0.652920\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": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\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>-0.015974</td>\n",
       "      <td>0.652920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>-0.215394</td>\n",
       "      <td>-0.352673</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B\n",
       "a -0.015974  0.652920\n",
       "c -0.215394 -0.352673"
      ]
     },
     "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": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\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>-0.015974</td>\n",
       "      <td>0.652920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>0.367530</td>\n",
       "      <td>0.852663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>-0.215394</td>\n",
       "      <td>-0.352673</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B\n",
       "a -0.015974  0.652920\n",
       "b  0.367530  0.852663\n",
       "c -0.215394 -0.352673"
      ]
     },
     "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": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\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>-0.015974</td>\n",
       "      <td>0.652920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>0.367530</td>\n",
       "      <td>0.852663</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B\n",
       "a -0.015974  0.652920\n",
       "b  0.367530  0.852663"
      ]
     },
     "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": {},
   "outputs": [],
   "source": [
    "resp = nsfg.ReadFemResp()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a27be7710>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution goes here\n",
    "hist = thinkstats2.Hist(resp.numkdhh, label='numkdhh')\n",
    "thinkplot.Hist(hist)\n",
    "thinkplot.Config(xlabel='Number of children', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a27bcb150>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution goes here\n",
    "pmf = thinkstats2.Pmf(resp.numkdhh, label='actual')\n",
    "biased_pmf = BiasPmf(pmf, label='observed')\n",
    "thinkplot.PrePlot(2)\n",
    "thinkplot.Pmfs([pmf, biased_pmf])\n",
    "thinkplot.Config(xlabel='Number of children', ylabel='PMF')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual mean 1.02420515504\n",
      "Observed mean 2.40367910066\n"
     ]
    }
   ],
   "source": [
    "# Solution goes here\n",
    "print('Actual mean', pmf.Mean())\n",
    "print('Observed mean', biased_pmf.Mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exercise 3.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here\n",
    "def PmfMean(pmf):\n",
    "    pmf_mean = 0.0\n",
    "    for xi, pi in pmf.d.items():\n",
    "        pmf_mean += xi*pi\n",
    "    return pmf_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here\n",
    "def PmfVar(pmf):\n",
    "    pmf_var = 0.0\n",
    "    pmf_mean = PmfMean(pmf)\n",
    "    for xi, pi in pmf.d.items():\n",
    "        pmf_var += pi * (xi - pmf_mean)**2\n",
    "    return pmf_var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean from pmf 1.02420515504\n",
      "My calculated mean 1.02420515504\n",
      "Variance from pmf 1.41286432635\n",
      "My calculated variance 1.41286432635\n"
     ]
    }
   ],
   "source": [
    "# Solution goes here\n",
    "print('Mean from pmf', pmf.Mean())\n",
    "print('My calculated mean', PmfMean(pmf))\n",
    "print('Variance from pmf', pmf.Var())\n",
    "print('My calculated variance', PmfVar(pmf))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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 two 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": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "live, firsts, others = first.MakeFrames()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "preg_map = nsfg.MakePregMap(live)\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here\n",
    "lngth_diff = np.array([])\n",
    "for caseid, idx in preg_map.items():\n",
    "    if len(idx) > 1:\n",
    "        tmp_first = preg.loc[idx[0]].prglngth\n",
    "        other_lngth = preg.loc[idx[1]].prglngth\n",
    "        lngth_diff = np.append(lngth_diff,other_lngth - tmp_first)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a2c64a990>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution goes here\n",
    "hist = thinkstats2.Hist(lngth_diff, label='lngth_diff')\n",
    "thinkplot.Hist(hist)\n",
    "thinkplot.Config(xlabel='Length Difference (weeks)', ylabel='Count')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.056367432150313153"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution goes here\n",
    "lngth_diff.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": 77,
   "metadata": {},
   "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": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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itkTEG8BtQFtBnTZgeeSsA4ZLGhUR2yLiEYCI+A9ya76PzrCtZma2l7IMJKOBZ/O2u3hnMChbR9JYcuu3/zyv+LKUClsmaUR/NdjMzPqurh+2SzoYuAO4PCJeTsVLgCOBqcA24Hsljp0nqUNSR3d394C018ysGWUZSLYCR+Rtj0llFdWRNJRcELklIn7YUyEinouItyJiF3ADuRTaO0TE0ohojYjWlpaWqi/GzMyKyzKQPAyMlzRO0n7AOcCqgjqrgAtS760ZwI6I2CZJwE3A5oj4+/wDJI3K2zwL2JjdJZiZWTmZ9dqKiJ2SFgD3AEOAZRGxSdL8tL8dWA2cBnQCrwIXp8NPAM4HHpf0aCr7ekSsBr4jaSoQwNPAn2d1DWZmVl6mc22lv/hXF5S1530O4NIix/0boBLfeX4/N9PMzKrgSRut7uSv4TGY9HVtFa9ZYo2irnttWfOoZA2PRtfXtVW8Zok1CgcSqwuVrOHR6Pq6torXLLFG4dSW1YVGXMOjmhRc/toqy1c+1J/NMhtwviMx64NmSMGZ9ZUDiVkfNEMKzqyvnNoy64OsU3CDtceaDW6+IzGrMafLrNE5kJjVmNNl1uic2jKrsUbssWaWz3ckZnWk2ADF3gYtmtUDBxKzOlKY5vKDd2sEvaa2JH0/Ii5Kny+MiJsHpFVmTSo/zZXPgxatnpW7I8n/P3phlg0xM7PGVC6QxIC0wszMGla5XltjJC0mtzZIz+fdIuJLmbXMGpqnQDdrHuXuSK4E1gMdeZ/zX72SNFvSk5I6JS0qsl+SFqf9GyRNS+VHSHpA0hOSNklamHfMSElrJD2V3kdUfrk2UDwFulnz6PWOpJqH65KGANcDpwBdwMOSVkXEE3nV5gDj0+t4YEl63wl8OSIekXQIsF7SmnTsIuD+iLg6BadFwFV7207LhqdAN2se5Xptreptf0Sc2cvu6UBnRGxJ33Ub0AbkB5I2YHlacnedpOGSRkXENmBbOsd/SNoMjE7HtgEnpeNvBtbiQNIw+rpKoPXOKUSrB+WekXwYeBa4Ffg5JdZRL2F0OrZHF7m7jXJ1RpOCCICkscAx6fwAh6dAA/A74PBiJ5c0D5gH8P73v78PzbYs9XWVQOtdqRSiA4kNpHLPSN4LfB04GriWXJrq+Yj414j416wbJ+lg4A7g8oh4uXB/upMp2rMsIpZGRGtEtLa0tGTcUqtUX1cJtN45hWj1oNwzkreAu4G7Je0PnAuslfStiPjHMt+9FTgib3tMKquojqSh5ILILRHxw7w6z/WkvySNAraXaYdlpFiaqi+BIX+VQDNrXGWnSJG0v6RPAv8MXAosBu6s4LsfBsZLGidpP+AcoPCZyyrggtR7awawIwUIATcBmyPi74scc2H6fCGwsoK2WAaKpamK9c7y/FFmg1uvgUTScuAhYBrwrYg4LiL+JiIK7yzeISJ2AguAe4DNwO0RsUnSfEk9/xRdDWwBOoEbgEtS+QnA+cBMSY+m12lp39XAKZKeAk5O21YDpVIoheWeP8pscCv3sP084A/kpkdZKKnneYTIPaJ4V28HR8RqcsEiv6w973OQu8spPO7fKPFgPyJeAGaVabcNsDuunV9yCvRS80eZ2eBQ7hmJZwc2K2H//YaW7YFWSR2zRlcutTVM0uWS/lHSPEleCMssqSRl57SeNYNygeFm4E3gp8BpwIfwLMBmQGUpO6f1rBmUCyQTI2ISgKSbgF9k3yQzM2sk5Z6B7E7upl5YZmZmb1PujmSKpJ4R5QIOSNsV9doyM7PBr1yvrSED1RAzM2tM7t5rZmZVcSAxM7OqeFyIWYOZu7Dd41GsrviOxKwBFI6G99LFVk8cSMwaQOEIefC6I1Y/nNoyawD5I+RLTY5pViu+IzEzs6o4kJiZWVUyDSSSZkt6UlKnpEVF9kvS4rR/g6RpefuWSdouaWPBMd+UtLXIgldmZlYDmQUSSUOA64E5wETgXEkTC6rNAcan1zxgSd6+7wOzS3z9NRExNb1Wl6hjDcpL85o1lizvSKYDnRGxJSLeAG4D2grqtAHLI2cdMFzSKICIeBD4fYbtszrlNTzMGkuWvbZGA8/mbXcBx1dQZzSwrcx3XybpAqAD+HJEvFhlW62OeA0Ps8bSiA/blwBHAlPJBZzvFauUVnTskNTR3d09kO0zM2sqWQaSrcARedtjUllf67xNRDwXEW9FxC7gBnIptGL1lkZEa0S0trS09LnxZmZWmSwDycPAeEnjJO0HnAOsKqizCrgg9d6aAeyIiF7TWj3PUJKzgI2l6pqZWfYye0YSETslLQDuAYYAyyJik6T5aX87sJrcWvCdwKvAxT3HS7oVOAk4TFIX8NcRcRPwHUlTgQCeBv48q2swM7PyMp0iJXXNXV1Q1p73OYBLSxx7bony8/uzjWZmVp1GfNhuZmZ1xIHEzMyq4kBiZmZVcSAxM7OqOJCYmVlVHEjMzKwqXiHRbBCau7B992SXnrfMsuY7ErMGU2qa/WJruq/4ccdANcuamAOJWYMpNc1+YTnkgolZ1pzaMmswvU2z31M+d2F70f1mWfAdiZmZVcWBxMzMquJAYmZmVXEgMTOzqjiQmJlZVdxry2yQ8+BEy1qmdySSZkt6UlKnpEVF9kvS4rR/g6RpefuWSdouaWPBMSMlrZH0VHofkeU1mDUiD060gZRZIJE0BLgemANMBM6VNLGg2hxgfHrNA5bk7fs+MLvIVy8C7o+I8cD9advM8nhwog2kLFNb04HOiNgCIOk2oA14Iq9OG7A8Lbm7TtJwSaMiYltEPChpbJHvbSO3ljvAzcBa4KpMrsCsQeUPWswfnLjyJ4+x4scdu4OKU17WH7JMbY0Gns3b7kplfa1T6PCI2JY+/w44vJpGmjWT/CACTnlZ/2joXlvpTiaK7ZM0T1KHpI7u7u4BbplZfSqW3nLKy6qVZSDZChyRtz0mlfW1TqHnJI0CSO/bi1WKiKUR0RoRrS0tLX1quJmZVS7LZyQPA+MljSMXHM4BPlNQZxWwID0/OR7YkZe2KmUVcCFwdXpf2a+ttl4V5thtcPCzE6tGZnckEbETWADcA2wGbo+ITZLmS5qfqq0GtgCdwA3AJT3HS7oVeAg4SlKXpM+nXVcDp0h6Cjg5bdsAKRZEiq2PYY3Fz06sGpkOSIyI1eSCRX5Ze97nAC4tcey5JcpfAGb1YzOtD4oFkU/Paa1Ra6y/+NmJVcMj222v3XHt/PKVrKF5VLxVoqF7bZlZ//OoeOsrBxIzexuPire+cmrLzN6m1Kh4s1J8R2L9pljvLffoMhv8HEis3xSmRNyjy6w5OLVlZVU6CDE/JWJmzcN3JFaWByGaWW8cSKwsD0I0s944tWV94kGIZlbIdyRmZlYVBxIzM6uKU1tWlKeLt0Keat5K8R2JFeWeWlbIU81bKQ4kVpR7alkhTzVvpTi1ZWW5p5ZVy2mxwS3TOxJJsyU9KalT0qIi+yVpcdq/QdK0csdK+qakrZIeTa/TsrwGs8FqIOdGc1pscMsskEgaAlwPzAEmAudKmlhQbQ4wPr3mAUsqPPaaiJiaXqsxsz4byLnRnBYb3LJMbU0HOiNiC4Ck24A24Im8Om3A8rTk7jpJwyWNAsZWcKz1M/fUai6eG836S5aprdHAs3nbXamskjrljr0spcKWSRpR7OSS5knqkNTR3d29t9fQVNxTywp5aQCrRCP22loCHAlMBbYB3ytWKSKWRkRrRLS2tLQMZPsalntqWSEvDWCVyDK1tRU4Im97TCqrpM7QUsdGxHM9hZJuAO7qvyY3n1LpLPfUMiid/lq+8qF+P5d7djWuLO9IHgbGSxonaT/gHGBVQZ1VwAWp99YMYEdEbOvt2PQMpcdZwMYMr2HQczpr8GuU9JR7djWuzAJJROwEFgD3AJuB2yNik6T5knr+ubsa2AJ0AjcAl/R2bDrmO5Iel7QB+FPgiqyuoRk4nTX4NUp6yj27GlemAxJT19zVBWXteZ8DuLTSY1P5+f3cTEuczhqcBrJ3Vqn0lA1ujfiw3czqlNNTzcmBxMz6jdNTzclzbTUhDzy0ejF3YbvTX4OA70iakHtqWS0V/r/m9FfjcyBpQu6pZbVU2IsMnP5qdE5tNTn31LKBlt+LbO7C9jK1rRE4kNS5akb7uiumDYSsn7nlP0fxKPf65NRWnaumO6W7YtpAyOKZm5+jNBYHkjpXTXdKd8W0gZDFMzc/R2ksTm3tBU8uZ1Zc/jO3aiZ2bJTnKP67IMd3JHvBKSNrdo0yEWTW/HdBjgPJXnDKyJpdo0wEmTX/XZDj1FaDck8Wq6VaLdPbW0/Eek0xlWrz/33gMV58+VVGvOtAbvybC/p0bG/X9WffWF72e/ub70gaiHuyWCPJIv1VKpVUzymmUm178eVXAXa/9+XY3lTyvf3NgaSBuCeLNZIs0l+lUkn1nGJqhp6Xmaa2JM0GrgWGADdGxNUF+5X2nwa8ClwUEY/0dqykkcAKYCzwNHB2RLyYRfv7OqCvv9JNpQZ4lerJUjjxnSdktHpQq/RXvt7+bPQlLdbXQZd9nYwyq1T1QKXAM7sjkTQEuB6YA0wEzpU0saDaHGB8es0DllRw7CLg/ogYD9yftjNRyW1lFummSgZ4lTpvqWPdy8bqUSX/X5aqU2l5ufRXJX/OywWR3s5bqazScQOR5ssytTUd6IyILRHxBnAb0FZQpw1YHjnrgOFpTfbejm0Dbk6fbwY+kdUFVHJbmUW6qZIBXqXOW+pY97KxelTJ/5el6lRaDr2nvyr5c14uiPR23r7IKpOQdYZCudVuM/hi6VPA7Ij4s7R9PnB8RCzIq3MXcHVE/Fvavh+4ilzaquixkl6KiOGpXMCLPdultLa2RkdH3yNyJQOh8gdgZTFwqpJJFUud1xMyWrOrtz+TtbQ3fx9IWh8RZf/F2dAP29Oa70UjoaR5kjokdXR3d1d9rr29Be/vc1Zaz2krs+rTYpV830Cdt69/pgfy74AsA8lW4Ii87TGprJI6vR37XEp/kd63Fzt5RCyNiNaIaG1padnri+ixN7fg1ehL6slpK7Pi+iMtVlinVufty98vA/13QJaprX2B/wfMIhcEHgY+ExGb8uqcDiwg12vreGBxREzv7VhJfwe8EBFXS1oEjIyIr/bWlr1NbZmZNbNKU1uZdf+NiJ2SFgD3kOvCuywFgvlpfzuwmlwQ6STX/ffi3o5NX301cLukzwO/Ac7O6hrMzKy8zO5I6onvSMzM+q4pHrabmVntOZCYmVlVHEjMzKwqDiRmZlYVBxIzM6tKU/TaktRNrqtwIzoMeL7WjagT/i328G+xh3+LPfr7t/hPEVF2RHdTBJJGJqmjku53zcC/xR7+Lfbwb7FHrX4Lp7bMzKwqDiRmZlYVB5L6t7TWDagj/i328G+xh3+LPWryW/gZiZmZVcV3JGZmVhUHkjomaYikX6aVJJuapOGSfiDpV5I2S/pwrdtUK5KukLRJ0kZJt0oaVus2DRRJyyRtl7Qxr2ykpDWSnkrvI2rZxoFS4rf4u/RnZIOkOyX1unpsf3EgqW8Lgc21bkSduBa4OyI+CEyhSX8XSaOBLwGtEXE0uWUWzqltqwbU94HZBWWLgPsjYjxwf9puBt/nnb/FGuDoiJhMbk2nrw1EQxxI6pSkMcDpwI21bkutSXo3cCJwE0BEvBERL9W2VTW1L3BAWgDuQOC3NW7PgImIB4HfFxS3ATenzzcDnxjQRtVIsd8iIu6NiJ1pcx251WUz50BSv/4B+Cqwq9YNqQPjgG7gf6dU342SDqp1o2ohIrYC3wWeAbYBOyLi3tq2quYOj4ht6fPvgMNr2Zg68jngxwNxIgeSOiTpDGB7RKyvdVvqxL7ANGBJRBwD/IHmSV+8Tcr/t5ELru8DDpJ0Xm1bVT8i1w216buiSvoLYCdwy0Ccz4GkPp0AnCnpaeA2YKakf65tk2qqC+iKiJ+n7R+QCyzN6GTg1xHRHRFvAj8E/nON21Rrz0kaBZDet9e4PTUl6SLgDOCzMUDjOxxI6lBEfC0ixkRE7MqKAAAD1UlEQVTEWHIPUn8SEU37r86I+B3wrKSjUtEs4IkaNqmWngFmSDpQksj9Fk3Z8SDPKuDC9PlCYGUN21JTkmaTS4mfGRGvDtR59x2oE5lV6TLgFkn7AVuAi2vcnpqIiJ9L+gHwCLnUxS9popHdkm4FTgIOk9QF/DVwNXC7pM+Tm+X77Nq1cOCU+C2+BuwPrMn9O4N1ETE/87Z4ZLuZmVXDqS0zM6uKA4mZmVXFgcTMzKriQGJmZlVxIDEzs6o4kFjTk/QXaTbdDZIelXR8xudbK6noutpphuMj++EcY/NnhS3Y911JM6s9h1kPjyOxppamoz8DmBYRr0s6DNivRm35EDAkIrZkfKrrgBuAn2R8HmsSviOxZjcKeD4iXgeIiOcj4rcAkp6W9B1Jj0v6haQ/SeUtku6Q9HB6nZDKD0prRPwiTS7ZlsoPkHRbWkflTuCAEm35LHmjsiW9ktaX2CTpPknT093MFklnpjoXSVqZyp+S9Nd53zdE0g3p+HslHZCu8TfAoZLe258/pDUvBxJrdvcCR0j6f5L+l6T/UrB/R0RMAv6R3IzMkFsb5ZqIOA6Yy56p/v+C3HQ204E/Bf4uzVL8ReDViJhAbvTxsSXacgKQP1HnQen7PgT8B/A/gFOAs4D/nldvemrHZOC/5qXNxgPXp+NfSnV6PJLOZ1Y1p7asqUXEK5KOBT5K7i//FZIWRcT3U5Vb896vSZ9PBiamKSgA3iXpYOBUcpNtfiWVDwPeT24tlcXpfBskbSjRnFHkpsvv8QZwd/r8OPB6RLwp6XFgbF69NRHxAoCkHwIfAf4PuckdH0111hccs53c7MFmVXMgsaYXEW8Ba4G16S/pC8mtPgdvn5K85/M+wIyI+GP+96RJFOdGxJMF5ZU25TVywafHm3mzt+4CetJvu9KiVoXtKtx+Pa/sLd6eUhuWzmdWNae2rKlJOkrS+LyiqeQm/uvx6bz3h9Lne8lNItnzHVPTx3uAy1JAQdIxqfxB4DOp7GhyKahiNgN/sheXcUpat/wAcqsD/qyCYz4AFO3VZdZXDiTW7A4Gbpb0REo5TQS+mbd/RCpfCFyRyr4EtKbuwk8APbOr/g0wFNggaVPaBlgCHCxpM7lnG6UWLPsRudlc++oXwB3ABuCOiOjorbKkoeQCVq/1zCrl2X/NSkgLi7VGxPMDdL4DgAeAE1K6rZJjLiLXxgV9OM9Z5Lo7f2OvGmpWwHckZnUiIl4j16trdMan2hf4XsbnsCbiOxIzM6uK70jMzKwqDiRmZlYVBxIzM6uKA4mZmVXFgcTMzKriQGJmZlX5/4oMJhsmfGraAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a2bcbf790>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here\n",
    "def ObservedPmf(pmf,speed,label=None):\n",
    "    new_pmf = pmf.Copy(label=label)\n",
    "\n",
    "    for x, p in pmf.Items():\n",
    "        new_pmf[x] *= abs(x - speed)\n",
    "        \n",
    "    new_pmf.Normalize()\n",
    "    return new_pmf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9l7sfA1YA9Wn71APLPbAOOMvMznP3fe6+OYzhI2A70L9jf5qIiORTzqlBzKwn8BWCUsZA4D7g6Qjn7k9QndWqmaD0kGuf/sC+lOsPBEYQVImJiEhCcjV6LweGAc8B33f3NwsS1cnr9wWeBL7p7h9m2ecW4BaACy64oIDRiYhUllwjvWcRtC80Aq+Z2Yfhz0dmlvELPMVe4PyU5wPCbZH2MbMqgmTxc3d/KttF3P0Bd69199p+/frlCElERDorVxvGae5+esrPGeHP6e5+Ro5zbwAGm9kgM+sBzADSu+k+A3zdApcCB919X9h7aimw3d3v6eTfJiIieZSrSqoamAN8DtgKLHP3ligndveWsHH8BYJutcvcfZuZzQlfbyKo6rqaoDH9MDA7PHwMcD3wBzPbEm77jrs/15E/TkRE8idXo/fDwHHgVYIv9s8TVE9FEn7BP5e2rSnlsQO3ZThuLR0c8yGlJX0di9ZtIlK8ciWMoe7+twBmthRYH39IUgzSF/XJt+mTajMuGiQixStXwmj7tgirmGIOR4pFpmSRqVTQWanrWIhIaci5gFJKbygDeoXPjaBGKVfDt5SoTMli+qRalq96LaGIykfcpTeRuOSarbZboQKR4vXkvXPaHithdF22ZJHPEpxIHHKNwxCRPMuWLNSGI8Uu59QgIhKf1NIbqAQnxU0JQ8rS1Mamtrv2Um1cT/0bRIqBEoaUjfQ2gKPHjrPy+Y2JJYz0xu0oX/7Z/gaRYqCEIWUjfWwHZG4vKJRMseT68o/7b8iWxEq1FCaFpYQhZSN1bMfUxqYce8cv0xd9ri//uP+GTMlo+arXWL7qNSUPyUm9pERK2NTGJq6bt5RVL70Raf/2EpaqvyQXJQyRAsg0T1Zn585KP66zX/Rfr78s47lEslGVlEgB5HPurCjtHFEa3IutCk+KnxKGSAHkc+6sKF/0nWlwF8lFCUPaaI6j8tGZBneRXNSGIW2yzVArIgJKGJIi2wy1IiKgKinJIn2OIyl+mkpE4qYShkgJy1cXW5EoVMIQKWHFNh2Kph4pbyphSIfkcwCadF39uEt49K6biqYKUd15y5sShnTI9Em1pyQI1ZlLKnXnLW+qkpIOyecANBEpLUoYUvZKdTGlTGt8q/pPkqQqqQq36qU3uG7e0rKbS6gceg+p+k+KjUoYFa5cR3cXW++hzlD1nxQbJYwKV66juzUTa+epa6xko4QhbYqla2YpK4cJHLN1jVXCECUMqShxN4CXQxWfusZKNkoYUvbSexvFecdcrlV8+aQqr9KlhCFlL6kGcFXxZaYqr9KlhCFlTw3gxUVVXqVL4zBERCQSJQwREYlEVVIVqBy6fopI4amEUYHKoeuniBSeEkYFUtdPEekMVUlVOHX9FJGoVMIQEZFIYi1hmNlE4F6gG/Cguy9Me93C168GDgMN7r45fG0ZcA3wvrsPizPOSqCGbhHpqthKGGbWDVgMTAKGAtea2dC03SYBg8OfW4AlKa89BEyMK75Ko4ZuEemqOKuk6oCd7r7L3Y8BK4D6tH3qgeUeWAecZWbnAbj7K8C/xRhfRVFDt4h0VZxVUv2B91KeNwOjI+zTH9gX9SJmdgtB6YQLLrigU4FWGjV0S7psy8GqClNSlXyjt7s/4O617l7br1+/pMMRKUlaDlaiiLOEsRc4P+X5gHBbR/cRKTrZpuguRtlKD6myLQe7fNVrscYmpSXOEsYGYLCZDTKzHsAM4Jm0fZ4Bvm6BS4GD7h65OkokKdmm6C5GKj1IvsRWwnD3FjObC7xA0K12mbtvM7M54etNwHMEXWp3EnSrnd16vJk9BlwBnGtmzcCd7r40rnhFOqKUpujOVnroilIqYUn+xDoOw92fI0gKqduaUh47cFuWY6+NMzYR6bxSKmFJ/pR8o7eIFF4plbAkfzSXlIjEbmpjk6qtyoAShkgXRemFVInS35dSrrbK1mZTaeuQK2EUCf2HLF3TJ9WqATiD9PcFSrfaKlubTaV9PpUwikQc/yE14WBhxNELqRykvi9TG5ty7F3c1GYTUMJoRyHv+uP4D6kJB6WUpLZzKAEXJ/WSakepdx3UhIP5teqlN7hu3tKSv1suJuk3MKX2Gas0KmG0o5yKoZpwsOtUYsu/cmrnqARKGFKxOloFohJb/pVTO0clUMIoA5qmIbpsXT07WmeuEptUIiWMMlDqbS2FVM5VIBoPUro62sHm5gXL+fcPD3P2Gb158B+/XrA41ehdBsqprSVu9eMu4dG7birLEoJmpS1dHb3p+/cPD5/yu1BUwhApExoPUrpK5aZPCUNEItFA0PZlq1b61W/fSKT6KA5KGCISSbZuxUoggWzVSq3bCl19FAe1YYhIJOpW3L5SqVbqCpUwRKTDUjsNaN3vyqEShoiIRKKEISIikahKSgTNlCoShUoYUrE0U6pIx6iEIRWrnKcJKVdamTJZShhSsTRTam5JzU+VLTFoqdRkqUqqyE1tbOK6eUtZ9dIbSYciFSip+alyDYJLpVJh4aiEUYTyNQW3SFclNT+VEkN0heywoRJGEUq/qwN9WEQku0J12FAJowipbl2kPMVZGijETaUShkg7NENrblq4qWNKuYpZCQMtcSrZZZuhVU5K771ULp+fKDcLqSWGjijVGxAlDDq+2lW+ipWpyyxKcdIMrbmVysJNUcZw5EoSrTcLlbokshIG0XpkxNFzKallFqVzynFZ13LUlTEcuZJF681CpQ74VMKISKOCRYpXaqm/K2M4spUo028MK7VTihJGRIXqudRe/XjqhyJ12UeRctZeo3qcg/tUovw0jcMoIpnqx7NNkKfqLCk3mW6WWj8TmUaba7xS4amEUSSy3c10pCos011X6naJprM9XyS7KF1vs/W2aq9RvVKrhpKihFHkolaFZWuQ0xdfNJk6NWjp0fyJ0vW2VHpbVTIljDKQXjrRh67jMpXkUqmU1jVKBuVBCUOEU7/QNJBTJLNYE4aZTQTuBboBD7r7wrTXLXz9auAw0ODum6McKxIX3Q2LZBZbLykz6wYsBiYBQ4FrzWxo2m6TgMHhzy3Akg4cKyIiBRRnt9o6YKe773L3Y8AKoD5tn3pguQfWAWeZ2XkRjxURkQKKs0qqP/BeyvNmYHSEffpHPLYoqDufSGlL6jMc5brF9v1S8gP3zOwWM9toZhv379/f5fNlGzyUa598XzPqfuq9I5L9s9GR7bnOV6jrduQzXejPf5wJYy9wfsrzAeG2KPtEORYAd3/A3WvdvbZfv35dDjrKGsaZRph2Vkd64CS1vrJIsYs6Gry9UeLp+yR13ajfL0l8/s3d4zmxWXfgj8DfEXzZbwCuc/dtKft8BZhL0EtqNHCfu9dFOTaT2tpa37ixMqYZFhHJBzPb5O6RMk9sbRju3mJmc4EXCLrGLnP3bWY2J3y9CXiOIFnsJOhWO7u9Y+OKVUREcouthJEElTBERDqmIyWMkm/0FhGRwlDCEBGRSJQwREQkEiUMERGJRAlDREQiKateUma2H/hz0nF00rnAX5IOokjovThJ78VJei9Oyud78Z/cPdKo57JKGKXMzDZG7dpW7vRenKT34iS9Fycl9V6oSkpERCJRwhARkUiUMIrHA0kHUET0Xpyk9+IkvRcnJfJeqA1DREQiUQlDREQiUcIoAmbWzcx+b2ark44lSWZ2lpk9YWZvm9l2M7ss6ZiSYmbfMrNtZvammT1mZtVJx1QoZrbMzN43szdTtv0HM3vRzHaEv89OMsZCyfJe3BV+Rraa2dNmdlah4lHCKA6NwPakgygC9wK/dvf/DFxChb4nZtYfuB2odfdhBFP8z0g2qoJ6CJiYtu0O4J/dfTDwz+HzSvAQn34vXgSGuXsNwbpB8wsVjBJGwsxsAPAV4MGkY0mSmZ0JXA4sBXD3Y+7+QbJRJao70CtcTKw38C8Jx1Mw7v4K8G9pm+uBh8PHDwP/taBBJSTTe+Hua9y9JXy6jmBF0oJQwkjej4F/AE4kHUjCBgH7gZ+G1XMPmlmfpINKgrvvBe4G9gD7gIPuvibZqBL3WXffFz7+V+CzSQZTRG4Eni/UxZQwEmRm1wDvu/umpGMpAt2BkcASdx8B/JXKqXY4RVg/X0+QRP8j0MfMZiUbVfHwoGtnxXfvNLPvAi3Azwt1TSWMZI0BJpvZbmAFMM7MHkk2pMQ0A83u/nr4/AmCBFKJrgLedff97n4ceAr4LwnHlLT/Z2bnAYS/3084nkSZWQNwDTDTCzg2QgkjQe4+390HuPtAgkbNl9y9Iu8k3f1fgffM7OJw098BbyUYUpL2AJeaWW8zM4L3oiI7AKR4BrghfHwDsCrBWBJlZhMJqrEnu/vhQl67eyEvJpLD3wM/N7MewC5gdsLxJMLdXzezJ4DNBFUOv6eCRjmb2WPAFcC5ZtYM3AksBB43s5sIZqT+WnIRFk6W92I+0BN4MbifYJ27zylIPBrpLSIiUahKSkREIlHCEBGRSJQwREQkEiUMERGJRAlDREQiUcKQimFm3w1ngN1qZlvMbHTM13vZzDKuuxzOynthHq4xMHUm07TX7jazcV29hkgrjcOQihBOlX4NMNLdj5rZuUCPhGL5PNDN3XfFfKlFwD8BL8V8HakQKmFIpTgP+Iu7HwVw97+4+78AmNluM/uhmf3BzNab2efC7f3M7Ekz2xD+jAm39wnXKVgfTpRYH27vZWYrwrU8ngZ6ZYllJikjlc3sULjGwTYz+42Z1YWlk11mNjncp8HMVoXbd5jZnSnn62Zm/xQev8bMeoV/45+Bc8zsb/L5RkrlUsKQSrEGON/M/mhmPzGzL6W9ftDd/xb4vwQzCEOwPseP3H0UMJWTU9B/l2AalzrgSuCucGbdW4HD7j6EYETuF7LEMgZInXCyT3i+zwMfAf8T+DIwBfgfKfvVhXHUAP8tpbprMLA4PP6DcJ9Wm8PriXSZqqSkIrj7ITP7AvBFgi/5lWZ2h7s/FO7yWMrvH4WPrwKGhtMvAJxhZn2B8QSTRn473F4NXECwnsd94fW2mtnWLOGcRzCVe6tjwK/Dx38Ajrr7cTP7AzAwZb8X3f0AgJk9BYwFfkkwUeGWcJ9Nace8TzDjrUiXKWFIxXD3T4CXgZfDL+MbCFY0g1Ony259fBpwqbsfST1POCHgVHd/J2171FA+JkgyrY6nzDh6AmitNjsRLqCUHlf686Mp2z7h1Kqw6vB6Il2mKimpCGZ2sZkNTtk0nGASu1bTU36/Fj5eQzAhYus5hocPXwD+PkwcmNmIcPsrwHXhtmEEVUeZbAc+14k/48vh2ta9CFac+12EYy4CMvaiEukoJQypFH2Bh83srbCqaCjwvZTXzw63NwLfCrfdDtSG3XDfAlpnBP1HoArYambbwucAS4C+ZradoO0h28JYzxLMQNpR64Enga3Ak+6+sb2dzayKIDG1u59IVJqtVipeuIBVrbv/pUDX6wX8FhgTVpNFOaaBIMa5HbjOFIJuxAs6FahIGpUwRArM3T8m6EXVP+ZLdQf+T8zXkAqiEoaIiESiEoaIiESihCEiIpEoYYiISCRKGCIiEokShoiIRKKEISIikfx/5ZK1iY+2FEsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a17351d10>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution goes here\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": "2.7.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}