._exam_bonus

.gitignore

.ipynb_checkpoints

exam_bonus.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import division"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import random\n",
    "from collections import Counter\n",
    "from collections import namedtuple\n",
    "from collections import OrderedDict\n",
    "\n",
    "import statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.stats import binom\n",
    "import scipy.optimize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## First, let's create some helper functions.  For a given exam, there are N students, each of which chose to get either 2 or 6 bonus points.  We summarize this list of values into an ExamResult object.\n",
    "\n",
    "## If the number of 6s in that list is less than or equal to 10%, everybody gets their requested points.  If it's greater than, everybody gets 0 points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ExamResult = namedtuple('ExamResult', 'total mean num_choices counts')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def get_value(point_choices):\n",
    "    num_choices = len(point_choices)\n",
    "    counts = Counter(point_choices)\n",
    "    \n",
    "    is_gt_ten_pct = counts[6] > num_choices / 10\n",
    "    \n",
    "    if is_gt_ten_pct:\n",
    "        return ExamResult(total=0, mean=0, num_choices=num_choices, counts=counts)\n",
    "    else:\n",
    "        total_points= sum(point_choices)\n",
    "        return ExamResult(total=total_points,\n",
    "                     mean=total_points/num_choices,\n",
    "                     num_choices=num_choices,\n",
    "                     counts=counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now, we're going to work on simulating a given Exam.  We're assuming that the exam consists of N students, each of which picks 6 bonus points with probability p."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def flip(p):\n",
    "    \"\"\"\n",
    "    Returns True with probability p, else false\n",
    "    \"\"\"\n",
    "    assert 0 <= p and p <= 1\n",
    "    return True if random.random() < p else False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def generate_choices_assuming_fixed_prob(num_students, prob):\n",
    "    return [6 if flip(prob) else 2 for i in range(num_students)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For example, let's say there are 10 students and each picks 6 bonus points with 10% probability.  We can create a sincle instance of such an experiment:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ExamResult(total=0, mean=0, num_choices=10, counts=Counter({2: 7, 6: 3}))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random.seed(42)\n",
    "\n",
    "choices = generate_choices_assuming_fixed_prob(num_students=10, prob=0.10)\n",
    "get_value(choices)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's generalize this by creating a function that runs many such Exams.  For each exam, it creates an ExamSummary object and returns a list of such objects.\n",
    "\n",
    "## We'll also create a function to take a list of ExamSummaries and return the average number of points per student (averaged over the many experiments run)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def generate_multiple_exams(choice_generator, num_experiments):\n",
    "    return [get_value(choice_generator()) for i in range(num_experiments)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def mean_points_over_exams(exams):\n",
    "    return statistics.mean([value.mean for value in exams])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## So, let's take the 10 student example with a 10% probability and let's perform that exam 100 times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.716"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exams = generate_multiple_exams(lambda: generate_choices_assuming_fixed_prob(num_students=10, prob=0.10),\n",
    "                            num_experiments=100)\n",
    "mean_points_over_exams(exams)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## So, in the above, on average, a student averaged 1.71 bonus points (averaged over all students in a given exam and over 100 simulated exams)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## To generalize/abstract this, we're going iterate over various numbers of students.  For each, we're going to scan along the probabiltiy p of a student picking heads.  For each combination, we're going to determine the average points awarded to students"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def create_exams(p, num_students, num_experiments=1000):\n",
    "    \n",
    "    def exam_generator():\n",
    "        return generate_choices_assuming_fixed_prob(num_students, p)\n",
    "    \n",
    "    return generate_multiple_exams(exam_generator, num_experiments)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# We get more granularity for lower probabilities since that's where\n",
    "# most of the interesting data is\n",
    "probs = np.concatenate([np.arange(0, 0.20, 0.002), np.arange(0.20, 1.0, 0.01)])\n",
    "\n",
    "num_students = [1, 10, 20, 50, 100, 500, 1000]\n",
    "\n",
    "data = OrderedDict()\n",
    "data['prob'] = probs\n",
    "for num in num_students:\n",
    "    mean_points = [mean_points_over_exams(create_exams(p, num, num_experiments=2000)) for p in probs]\n",
    "    data['{} student{}'.format(num, 's' if num>1 else '')] = mean_points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "summary = pd.DataFrame(data)\n",
    "summary = summary.set_index('prob')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# We smooth from right to left since we're mostly interested in the left\n",
    "smoothed = pd.rolling_mean(summary[::-1], window=5)[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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oH330Effeey8A48aNo1+/fhiNRpYtW0bNmjV56623aNOmDbVq1bpi5Y2PP/6Y9PR0goOD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\nMzMza8nBs5mZmZlZSw6ezczMzMxa+hszaPNRG9GzeQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109e917d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,8))\n",
    "\n",
    "smoothed.plot(ax=plt.gca())\n",
    "\n",
    "plt.xlabel(\"Probability that a given student picks 6\")\n",
    "plt.ylabel(\"Average bonus points given per student\")\n",
    "plt.title(\"Num Experiments per point = 2000\")\n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.savefig(\"experiment_distribution.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# We use the un-smoothed values here\n",
    "optimal_probs = pd.DataFrame({'probability': pd.Series({col: summary.sort_values(by=col, ascending=False).index[0] for col in summary.columns}),\n",
    "                              'expected_points': pd.Series({col: summary.sort_values(by=col, ascending=False).iloc[0][col] for col in smoothed.columns})\n",
    "                              }).ix[summary.columns]                                                                                        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "scrolled": 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>expected_points</th>\n",
       "      <th>probability</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1 student</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10 students</th>\n",
       "      <td>2.044200</td>\n",
       "      <td>0.028</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20 students</th>\n",
       "      <td>2.074800</td>\n",
       "      <td>0.036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50 students</th>\n",
       "      <td>2.130320</td>\n",
       "      <td>0.038</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100 students</th>\n",
       "      <td>2.180960</td>\n",
       "      <td>0.052</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>500 students</th>\n",
       "      <td>2.267172</td>\n",
       "      <td>0.068</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1000 students</th>\n",
       "      <td>2.304034</td>\n",
       "      <td>0.078</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               expected_points  probability\n",
       "1 student             2.000000        0.000\n",
       "10 students           2.044200        0.028\n",
       "20 students           2.074800        0.036\n",
       "50 students           2.130320        0.038\n",
       "100 students          2.180960        0.052\n",
       "500 students          2.267172        0.068\n",
       "1000 students         2.304034        0.078"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wNDNfVWmEJTiTL0mTGxkZYWBgEatWLeGR+Z0RttxyEd/5zhKe85xSN0CXpJ5W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\nzMw6jIN8MzMzM7MO4yDfzMzMzKzD/B/2RMrMTASpyQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109e863d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "optimal_probs['probability'].plot(ax=plt.gca(),  style='-o')\n",
    "\n",
    "plt.xlabel(\"Number of students in the class\")\n",
    "plt.ylabel(\"Optimal probability given student picking 6\")\n",
    "\n",
    "plt.savefig(\"optimal_probability.png\")\n",
    "\n",
    "optimal_probs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Essentially, this table tells us, if we have N students in our class and if all students coordinate to pick \"6 points\" with a fixed probability, what that probability should be to maximize the average number of bonus points each student will receive (and what that maximum number of points is).\n",
    "\n",
    "If we have only 1 student, they should opt for 2 exam points every time (and get 6 exam points with probability 0).  This makes sense because if they were to pick 6 points, the average number of points in the class would surely be above 10%, and therefore they'd receive 0 points.  So, they max they can get is 2 points.\n",
    "\n",
    "If we have a class of 20 students who are offered the same game, the coordinating students should opt for the 6 point bonus only 2.6% of the time.  This is pretty rare.  Essentially, it means that, on average, no students will even get the bonus (about half the time, 1 student will get it).  In this example, the probability is low to ensure that the probability of 3 students getting the bonus remails low (which would be catestropic).  Since 20 students isn't very many, the probability of relatively large fluctuations in the number of students who end up getting 6 bonus points in our strategy is non-negligable.\n",
    "\n",
    "When the number of students becomes larger (say, 500 students in a large lecture), we can afford to be much more aggressive in letting a higher percentage of students get the bonus.  So, we are allowed to have students pick the 6 points at a rate greater than 7%, which is much more aggressive than we could with only 20 students.  In effect, the law of large numbers is protecting us from calamity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<table border=\"1\" class=\"dataframe\">  <thead>    <tr style=\"text-align: right;\">      <th></th>      <th>expected_points</th>      <th>probability</th>    </tr>  </thead>  <tbody>    <tr>      <th>1 student</th>      <td>2.000000</td>      <td>0.000</td>    </tr>    <tr>      <th>10 students</th>      <td>2.044200</td>      <td>0.028</td>    </tr>    <tr>      <th>20 students</th>      <td>2.074800</td>      <td>0.036</td>    </tr>    <tr>      <th>50 students</th>      <td>2.130320</td>      <td>0.038</td>    </tr>    <tr>      <th>100 students</th>      <td>2.180960</td>      <td>0.052</td>    </tr>    <tr>      <th>500 students</th>      <td>2.267172</td>      <td>0.068</td>    </tr>    <tr>      <th>1000 students</th>      <td>2.304034</td>      <td>0.078</td>    </tr>  </tbody></table>\n"
     ]
    }
   ],
   "source": [
    "print optimal_probs.to_html().replace('\\n','')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Let's look at the exact formula"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$<points> = \\sum_{n=0}^{\\lfloor(N/10)} Binom(n|p, N)(6n - 2(N-n))$$\n",
    ", where $\\lfloor$ is the floor function, ensuring that we only sum over values of n that are less than 10% of N.  We can thus calculate both the optimal number of"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def exp_points(p, N):\n",
    "    # Writing this in a vectorized form is much faster\n",
    "    # Trust me...\n",
    "    ns = np.array(range(0, N//10 + 1))\n",
    "    probabilities = binom.pmf(ns, N, p)\n",
    "    values = np.array([(6*n + 2*(N-n)) for n in ns])\n",
    "    return np.sum(np.dot(probabilities, values)) / N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.1717518387142407"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exp_points(N=100, p=0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def get_max_p(N, delta=0.001):\n",
    "    \n",
    "    def func(p):\n",
    "        return -1*exp_points(p=p, N=N)\n",
    "    \n",
    "    # We input the max bound of 0.2 by-hand becasue we know\n",
    "    # it'll never be optimal to go above it\n",
    "    # Plus, the optimization becomes unstable if we go past that bounds,\n",
    "    # as there's a discontinuity\n",
    "    res = scipy.optimize.minimize_scalar(func, method='bounded', bounds=[0.0, 0.2])\n",
    "    if not res.success:\n",
    "        print res\n",
    "        raise Exception(res)\n",
    "    opt_p = res.x\n",
    "    \n",
    "    return (opt_p, exp_points(p=opt_p, N=N))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.098907069008345866, 2.3953221315351594)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_max_p(N=1000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10ac17610>]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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0fnyxxcEf/lB2JZI0fIZ8C5yykdSrDPkWvPKV0KZtJCSpq5yTb8ETT8CMGfDww94UJan7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\nqcIMeUmqsP8H/1O6PxntAnEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109e91190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "XX = np.arange(0.0, 1.0, 0.01)\n",
    "YY = [exp_points(N=100, p=x) for x in XX]\n",
    "plt.plot(XX, YY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "XX = [1, 5, 10, 50, 100, 500, 1000, 5000, 10000, 50000, 100000, 500000, 750000, 1000000]\n",
    "vals = [get_max_p(N=x) for x in XX]\n",
    "df = pd.DataFrame({'probability': [val[0] for val in vals],\n",
    "                   'expected_points': [val[1] for val in vals]},\n",
    "                  index=XX)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>expected_points</th>\n",
       "      <th>probability</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.999990</td>\n",
       "      <td>0.000005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.999952</td>\n",
       "      <td>0.000005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2.034655</td>\n",
       "      <td>0.018183</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>2.123904</td>\n",
       "      <td>0.039783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>2.171762</td>\n",
       "      <td>0.050223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>500</th>\n",
       "      <td>2.268546</td>\n",
       "      <td>0.070979</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1000</th>\n",
       "      <td>2.299600</td>\n",
       "      <td>0.077683</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5000</th>\n",
       "      <td>2.348601</td>\n",
       "      <td>0.088398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10000</th>\n",
       "      <td>2.361969</td>\n",
       "      <td>0.091364</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50000</th>\n",
       "      <td>2.381452</td>\n",
       "      <td>0.095737</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100000</th>\n",
       "      <td>2.386464</td>\n",
       "      <td>0.096875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>500000</th>\n",
       "      <td>2.393545</td>\n",
       "      <td>0.098497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>750000</th>\n",
       "      <td>2.394652</td>\n",
       "      <td>0.098752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1000000</th>\n",
       "      <td>2.395322</td>\n",
       "      <td>0.098907</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         expected_points  probability\n",
       "1               1.999990     0.000005\n",
       "5               1.999952     0.000005\n",
       "10              2.034655     0.018183\n",
       "50              2.123904     0.039783\n",
       "100             2.171762     0.050223\n",
       "500             2.268546     0.070979\n",
       "1000            2.299600     0.077683\n",
       "5000            2.348601     0.088398\n",
       "10000           2.361969     0.091364\n",
       "50000           2.381452     0.095737\n",
       "100000          2.386464     0.096875\n",
       "500000          2.393545     0.098497\n",
       "750000          2.394652     0.098752\n",
       "1000000         2.395322     0.098907"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PNwCZeTVwdURMAY4q3z8A/Aj4Wfkg5WDnLo+I44GrKB7uPD0z50XEccXhPC0z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\nM7Mu4uTbzMzMzKyLOPk2MzMzM+si/w/wiaogNdHQ0gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ac1c710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "\n",
    "plt.subplot(2, 1, 1)\n",
    "YY = [val[0] for val in vals]\n",
    "df.probability.plot()\n",
    "plt.xscale('log')\n",
    "plt.ylim([0.0, 0.15])\n",
    "plt.axhline(0.10, linestyle='--', color='black')\n",
    "plt.xlabel(\"Number of students in class\")\n",
    "plt.ylabel(\"Probability for optimal number of points\")\n",
    "\n",
    "plt.subplot(2, 1, 2)\n",
    "df.expected_points.plot()\n",
    "plt.plot(XX, YY)\n",
    "plt.xscale('log')\n",
    "plt.ylim([2.0, 2.5])\n",
    "plt.axhline(2.4, linestyle='--', color='black')\n",
    "plt.xlabel(\"Number of students in class\")\n",
    "plt.ylabel(\"Average number of bonus points per student\")\n",
    "\n",
    "plt.savefig(\"prob_and_points_by_N.png\")\n",
    "\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<table border=\"1\" class=\"dataframe\">  <thead>    <tr style=\"text-align: right;\">      <th></th>      <th>expected_points</th>      <th>probability</th>    </tr>  </thead>  <tbody>    <tr>      <th>1</th>      <td>1.999990</td>      <td>0.000005</td>    </tr>    <tr>      <th>5</th>      <td>1.999952</td>      <td>0.000005</td>    </tr>    <tr>      <th>10</th>      <td>2.034655</td>      <td>0.018183</td>    </tr>    <tr>      <th>50</th>      <td>2.123904</td>      <td>0.039783</td>    </tr>    <tr>      <th>100</th>      <td>2.171762</td>      <td>0.050223</td>    </tr>    <tr>      <th>500</th>      <td>2.268546</td>      <td>0.070979</td>    </tr>    <tr>      <th>1000</th>      <td>2.299600</td>      <td>0.077683</td>    </tr>    <tr>      <th>5000</th>      <td>2.348601</td>      <td>0.088398</td>    </tr>    <tr>      <th>10000</th>      <td>2.361969</td>      <td>0.091364</td>    </tr>    <tr>      <th>50000</th>      <td>2.381452</td>      <td>0.095737</td>    </tr>    <tr>      <th>100000</th>      <td>2.386464</td>      <td>0.096875</td>    </tr>    <tr>      <th>500000</th>      <td>2.393545</td>      <td>0.098497</td>    </tr>    <tr>      <th>750000</th>      <td>2.394652</td>      <td>0.098752</td>    </tr>    <tr>      <th>1000000</th>      <td>2.395322</td>      <td>0.098907</td>    </tr>  </tbody></table>\n"
     ]
    }
   ],
   "source": [
    "print df.to_html().replace('\\n','')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}

experiment_distribution.png

optimal_probability.png

prob_and_points_by_N.png