brothers.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-05-23T16:38:30.231724",
     "start_time": "2016-05-23T16:38:30.094798"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from itertools import chain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-05-23T16:38:31.033168",
     "start_time": "2016-05-23T16:38:30.735832"
    },
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-05-23T16:38:57.318004",
     "start_time": "2016-05-23T16:38:31.551653"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0117380724123\n"
     ]
    }
   ],
   "source": [
    "res = []\n",
    "for _ in xrange(50000):\n",
    "    kids = np.random.randint(1,10,100)\n",
    "\n",
    "    boys = np.array([np.random.randint(0, 2, k).sum() for k in kids])\n",
    "    girls = kids-boys\n",
    "    \n",
    "    boy_brothers = [[b-1]*b for b in boys]\n",
    "    girl_brothers = [[b]*g for b, g in zip(boys, girls)]\n",
    "    \n",
    "    res.append(np.array(list(chain(*girl_brothers))).mean() - np.array(list(chain(*boy_brothers))).mean())\n",
    "print np.array(res).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-05-23T16:38:57.623985",
     "start_time": "2016-05-23T16:38:57.320849"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108b0f750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(res, bins=100)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
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   "codemirror_mode": {
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