{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Correlation and Regression to the Mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In [\"Thinking, Fast and Slow\"](https://en.wikipedia.org/wiki/Thinking,_Fast_and_Slow) by Daniel Kahneman, while explaining regression to the mean he writes,\n",
    "\n",
    "> Highly intelligent women tend to marry men who are less intelligent than they are.\n",
    "\n",
    "is equivalent to the statement\n",
    "\n",
    "> The correlation between the intelligence scores of spouses is less then perfect.\n",
    "\n",
    "He further clarifies his point.\n",
    "\n",
    "> If the correlation between the intelligence of spouses is less than perfect (and if men and women on average do not differ in intelligence), then it is a mathematical inevitability that highly intelligent women will be married to husbands who are on average less intelligent than they are (and vice versa, of course). The observed regression to the mean cannot be more interesting or more explainable than the imperfect correlation.\n",
    "\n",
    "Now I understand the point he is making and his book is not a textbook.\n",
    "If married couple's intelligence follows a bivariate normal distribution (which is likely I imagine) then this is true.\n",
    "I think it would be interesting to try generating discrete bivariate distribtions to see if I can find counter examples that show that Kahneman's statements are not equivalent.\n",
    "\n",
    "The tool I'll be using to do this is [convex optimization](https://en.wikipedia.org/wiki/Convex_optimization), although all the problems I'm doing are a subset, specifically [linear programming](https://en.wikipedia.org/wiki/Linear_programming).\n",
    "My tool of choice in python is [cvxpy](http://www.cvxpy.org/en/latest/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "figsize(12, 8)\n",
    "import cvxpy as cvx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I need to compute the [correlation coefficient](https://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient) over discrete bivariate distributions to check if the claims have been violated.\n",
    "I'm defining [covariance](https://en.wikipedia.org/wiki/Covariance) and correlation here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def covariance(mat):\n",
    "    XY = np.maximum(mat.value.A, 0)\n",
    "    N = len(XY)\n",
    "    XYv = np.outer(np.arange(N), np.arange(N))\n",
    "    EXY = (XY * XYv).sum()\n",
    "\n",
    "    EX = np.dot(XY.sum(axis=1), np.arange(N))\n",
    "    EY = np.dot(XY.sum(axis=0), np.arange(N))\n",
    "\n",
    "    return EXY - EX*EY\n",
    "\n",
    "def correlation(mat):\n",
    "    XY = np.maximum(mat.value.A, 0)\n",
    "    N = len(XY)\n",
    "    cov = covariance(mat)\n",
    "    \n",
    "    xx = XY.sum(axis=1)\n",
    "    yy = XY.sum(axis=0)\n",
    "    \n",
    "    EX = np.dot(xx, np.arange(N))\n",
    "    EY = np.dot(yy, np.arange(N))\n",
    "    \n",
    "    varX = np.dot(xx, (np.arange(N) - EX)**2)\n",
    "    varY = np.dot(yy, (np.arange(N) - EY)**2)\n",
    "        \n",
    "    return cov / np.sqrt(varX * varY)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'm going to generate a 20x20 matrix to represent the bivariate distribution.\n",
    "Columns will represent wife intelligence and rows will represent husband intelligence, so bright people will be in the last 10 columns and rows, while dim people will be in the first 10 columns and rows.\n",
    "I also create a few expressions I'll be using in the linear program, such as the [marginal probabilities](https://en.wikipedia.org/wiki/Marginal_distribution) and [expected values](https://en.wikipedia.org/wiki/Expected_value) of bright women (women who fall in the last 10 columns)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "N = 20\n",
    "# joint probability matrix\n",
    "# rows are husband intelligence\n",
    "# columns are wife intelligence\n",
    "prob = cvx.Variable(N, N)\n",
    "\n",
    "# marginal probability distributions\n",
    "prob_women = (np.ones(N) * prob).T\n",
    "prob_men = prob * np.ones(N)\n",
    "\n",
    "# expected value of men and women intelligence\n",
    "exp_women = prob_women.T * np.arange(N)\n",
    "exp_men = prob_men.T * np.arange(N)\n",
    "\n",
    "# expected values of smart women and men given they are married to smart women\n",
    "exp_bright_women = np.arange(N//2, N) * prob_women[N//2:] / .5\n",
    "exp_men_given_bright_women = np.arange(N) * prob[:, N//2:] * np.ones(N//2) / .5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'll construct the constraints, first the probability matrix must sum to 1 and must be nonnegative."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "constraints = [cvx.sum_entries(prob) == 1., prob >= 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to make the conditional expectation expressions correct, I need to make the probability of bright women and men equal to the probability of dim women and men.\n",
    "To make them equal, I add a median constraint."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "constraints.extend([cvx.sum_entries(prob_women[:N//2]) == cvx.sum_entries(prob_women[N//2:]),\n",
    "                    cvx.sum_entries(prob_men[:N//2]) == cvx.sum_entries(prob_men[N//2:])])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now Kahneman says this is the case \"if men and women on average do not differ in intelligence\", I'm going to interpret this as the expected women's intelligence is equal to the expected men's intelligence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "constraints.append(exp_women == exp_men)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's enough constraints to get us started.\n",
    "Now there is the question of what quantity to maximize since this is an opimization problem.\n",
    "The objective will be to subtract the expected intelligence of bright women from the expected intelligence of men that have married bright women.\n",
    "If this quantity is positive then Kahneman's \"regression to the mean\" will be violated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "objective = cvx.Maximize(exp_men_given_bright_women - exp_bright_women)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now it's a simple matter of running it through cxvpy by giving it the objective and the constraints and letting it solve the problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'optimal'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "problem = cvx.Problem(objective, constraints)\n",
    "problem.solve()\n",
    "problem.status"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the status is \"optimal\" that means all constraints are met and the problem is solved.\n",
    "The status is \"optimal\" so we can proceed with analysis.\n",
    "Let's first check the objective value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.9999999993702"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "objective.value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's 9!\n",
    "The only way this can happen is if all the bright women (women above or equal to 10 intelligence) are 10 and they are all married to men with intelligence of 19.\n",
    "Let's look at the probability distributions to see what happened."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_marginal(marginal):\n",
    "    plt.plot(100. * marginal.value, '-o')\n",
    "    plt.ylabel('probability (percentage)')\n",
    "    plt.xlabel('intelligence')\n",
    "    plt.ylim(0, 100. * marginal.value.max() * 1.1)\n",
    "\n",
    "def plot_joint(joint):\n",
    "    mat = np.maximum(100. * joint.value.A, 0)\n",
    "    #mat = np.log(np.maximum(np.log(joint.value.A), 0) + 1)\n",
    "    plt.imshow(mat, interpolation='none')\n",
    "    plt.colorbar()\n",
    "    plt.ylabel('men')\n",
    "    plt.xlabel('women')\n",
    "    plt.grid(False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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qrUlur6oLkzyY5M59eG8A4BlipaGmux9N8qrl44eTvHaV7wcAnDvLTwAAI9qP5ScAYELm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\nNMfKT51L8jIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e05deb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_joint(prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see here that all the mass for bright women is of women with 10 intelligence marrying men of 19 intelligence.\n",
    "Let's see what happened to the marginals. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EcU7n+B7gl4A1Bl3oZeDeMcZHZFybJM3EqBNtWEwdPObOEC1JdzbOhYX/Cbgd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\n8GVLmxmxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e141198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_marginal(prob_women)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IV4/dvw/wpTnVMxejn5JG8zuSJEk6PTvRx3Sihx1ngKuAj4cQ3sNgJvo64M/n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\nkqQp/f9R+s5fbc+qwwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e57c860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_marginal(prob_men)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see now that the marginal distributions for both men and women are quite binary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99999999716406629"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is perfectly correlated.\n",
    "Let's add a constraint to make the distribution look [unimodal](https://en.wikipedia.org/wiki/Unimodality) since I think that would be a better representation of an intelligence distribution.\n",
    "To do this I'll add a constraints that will enforce the maximum value to occur at 9 or 10 and make it unimodal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "prob_const = 0\n",
    "constraints.extend([cvx.diff(prob_men[:N//2]) >= prob_const,\n",
    "                    cvx.diff(prob_women[:N//2]) >= prob_const,\n",
    "                    cvx.diff(prob_men[N//2:]) <= -prob_const,\n",
    "                    cvx.diff(prob_women[N//2:]) <= -prob_const])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'optimal'"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "problem = cvx.Problem(objective, constraints)\n",
    "problem.solve()\n",
    "problem.status"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.49999999907409"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "objective.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pEnDOSHJVkr/Ztt2tGgCAUdpNwPmRJE/p7gePd/CqekGSN3X3i6vq6UnelmQjyaeS/Fx3\nbx7vmADAcq3iNPETbTef4PNJnny8A1fV6zM7veux803XJrm6u8/PbJHyDx/vmAAAu7GbBidJPlNV\nn0ryjfnzze6+cIfvuTvJq5L8/vz5Od19+/zxnyb5V5mdfg4AjMipsgbn1x5h245TS939zqo6c8um\nrf9rfTWztT0AACfcjgGnuz90gt5rY8vjA0n+7gSNCwCcQFNocPZyFdEdVXXB/PEPJrl90YsBgNVY\nxd3ET7TdrsF5NI5OZ/1CkkNV9Zgkn0nyjj14bwDgFLTUgNPd9yR54fzx55L8i2W+HwDw6JmiAgAY\nob2YogIATiKnyoX+AABOKhocAGBgCmtwBBwAYGAKAccUFQAwORocAGBgCg2OgAMnsWX9Edrc3PF2\ncwCjJuAAAANOEwcAGCENDgAwYA0OADA5Uwg4pqgAgMnR4AAAAxocAIAR0uAAAANTaHAEHABgwHVw\nAABGSIMDAAxMYYpKgwMATI4GBwAY0OAAAIyQBgcAGJhCgyPgAAADThMHABghDQ4AMLCKKaqq2p/k\nxiRPTfLYJL/a3e/Zsv/iJG9I8lCSG7v7+kXjaXAAgDH48ST3dff5Sf51kt88umMefq5NclGSC5Jc\nXlVPWTSYBgcAGFjRIuM/TvKO+eP1zJqao85Kcnd3H06SqvpIkvO3vP4fEHAAgJXr7geSpKoOZBZ2\nfmnL7tOTHN7y/CtJzlg0noADAAys6jTxqvq+JO9M8lvd/Ydbdh1OcmDL8wNJ7l80loADAAysaJHx\ndyR5X5Kf7e7btu3+bJJnVNWTkjyQ2fTUNYvGE3AAgDG4OrNppzdW1Rvn2w4leWJ3H6qq1yW5NbP1\nOTd0972LBlvb3Nxc6tE+SqM+OFi1Zf3+7tu3bynjbmxsLGVcmJBRXEL41ltvXcofl5e+9KV79vmc\nJg4ATI4pKgBgYAr3otLgAACTo8EBAAam0OAIOADAwBQCjikqAGByNDgAwMD6+snff5z8nwAAYBsN\nDgAwYA0OAMAICTgAwOSYogIABkxRAQCMkAYHABjQ4AAAjJAGBwAY0OAAAIyQBgcAGJhCgyPgAAAD\nUwg4pqgAgMnR4AAAAxocAIAR0uAAAAMaHACAERJwAIDJMUUFAAyYogIAGCENDgAwoMEBABghDQ4A\nMKDBAQAYIQ0OADAwhQZHwAEABqYQcExRAQCTo8EBAAY0OAAAI6TBAQAGptDgCDgAwChU1QuSvKm7\nX7xt+5VJLkty33zTwe6+a9FYAg4AsHJV9fokP5Hkq4+w+5wkl3T3HbsdzxocAGBgbW1tKV87uDvJ\nq5I80gvPTXJ1VX24qq7azWcQcACAlevudyZ56Bi7b0pyMMmFSc6rqpftNJ6AAwAMrKjBWeQt3f2l\n7j6S5OYkZ+/0DdbgAACjVVVnJLmzqp6V5GuZtTg37PR9Ag4AMLDi08Q3k6SqXp3ktO4+NF93c1uS\nryd5f3ffstMga5ubm8s9zEdn1AcHq7as3999+/YtZdyNjY2ljAsTMooL0Hzyk59cyh+X5z73uXv2\n+TQ4AMCAC/0BAJMzhYDjLCoAYHI0OADAgAYHAGCENDgAwMAUGhwBBwAYmELAMUUFAEyOgAMATI6A\nAwBMjjU4AMCANTgAACOkwQEABqbQ4Ag4AMDAFAKOKSoAYHI0OADAgAYHAGCENDgAwIAGBwBghDQ4\nAMCABgcAYIQEHABgckxRAQADpqgAAEZIgwMADEyhwVlqwKmqFyR5U3e/uKrOTvKeJJ+b776uu/9o\nme8PAJyalhZwqur1SX4iyVfnm85Ncm13X7us9wQASJbb4Nyd5FVJfn/+/Nwkz6yqH86sxfl33f3V\nY30zALAaU5iiWtoi4+5+Z5KHtmz6WJJf7O4Lknwhya8s670BgFPbXi4yfld3H54/fneS39jD9wYA\ndkmDc3xuqarnzx+/JMnH9/C9AYBTyF40OJvz/16R5Leq6kiSe5NcvgfvDQAcpyk0OGubm5s7v2p1\nRn1wsGrL+v3dt2/fUsbd2NhYyrgwIaNIFvfcc89S/riceeaZe/b5XMkYAJgcVzIGAAamMEWlwQEA\nJkeDAwAMrKrB2XqLp23bL07yhsyur3djd1+/01gaHABg5ea3eDqU5LHbtu9Pcm2Si5JckOTyqnrK\nTuMJOADAGBy9xdP2+uisJHd39+HuPpLkI0nO32kwAQcAWLlHuMXTUacnObzl+VeSnLHTeNbgAAAD\nIzuL6nCSA1ueH0hy/07fJOAAAAMjCzifTfKMqnpSkgcym566ZqdvEnAAgDHZTJKqenWS07r7UFW9\nLsmtmS2tuaG7791pELdqgJOYWzXA5IyiOvniF7+4lD8u3/M93+NWDQAA3yoBBwCYHAEHAJgci4wB\ngIGRnUX1LRFwAICBKQQcU1QAwORocACAAQ0OAMAICTgAwOQIOADA5FiDAwAMTGENjoADAAxMIeCY\nogIAJkfAAQAmR8ABACbHGhwAYMAaHACAEdLgAAADU2hwBBwAYGAKAccUFQAwOQIOADA5Ag4AMDnW\n4AAAA9bgAACMkAYHABjQ4AAAjJCAAwBMjikqAGDAFBUAwAhpcACAAQ0OAMAICTgAwOSYogIABkxR\nAQCMkIADAEyOgAMATI41OADAwBTW4Ag4AMDKVdV6kt9O8uwkX0/y0939+S37r0xyWZL75psOdvdd\nxxpPwAEAxuAVSR7T3S+sqhckefN821HnJLmku+/YzWDW4AAAA2tra0v52sGLktySJN39sSTP27b/\n3CRXV9WHq+qqnQYTcACAMTg9yZe3PH94Pm111E1JDia5MMl5VfWyRYMJOADAGHw5yYEtz9e7e2PL\n87d095e6+0iSm5OcvWgwAQcAGIOPJvmhJKmqH0hy59EdVXVGkv9eVU+sqrXMWpyPLxpsbXNzc4nH\n+qiN+uBg1Zb1+7tv376ljLuxsbHzi+DUNorzsx944IGl/HF54hOfeMzPNw8uR8+iSpJLM1t3c1p3\nH6qqVye5MrMzrN7f3f9+0XsJOHASE3Bgck7ZgHOimaICACbHdXAAgIEpXMlYgwMATI6AAwBMjoAD\nAEyONTgAwIA1OAAAIyTgAACTY4oKABgwRQUAMEICDgAwOQIOADA5Ag4AMDkWGQMAAxYZAwCMkIAD\nAEyOgAMATI41OADAgDU4AAAjJOAAAJNjigoAGDBFBQAwQgIOADA5Ag4AMDnW4AAAA9bgAACMkIAD\nAEyOKSoAYMAUFQDACAk4AMDkCDgAwORYgwMADFiDAwAwQgIOADA5pqgAgAFTVAAAIyTgAACTY4oK\nAFi5qlpP8ttJnp3k60l+urs/v2X/xUnekOShJDd29/WLxtPgAAADa2trS/nawSuSPKa7X5jkqiRv\nPrqjqvYnuTbJRUkuSHJ5VT1l0WACDgAwBi9KckuSdPfHkjxvy76zktzd3Ye7+0iSjyQ5f9Fgo56i\nOnLk4VUfAozc5lJGffazn7OUcf1Ow2L79+9b9SGs0ulJvrzl+cNVtd7dG/N9h7fs+0qSMxYNNuqA\ns3//vpP/PDU4CX3yk3es+hCA1VrFv79fTnJgy/Oj4SaZhZut+w4kuX/RYKaoAIAx+GiSH0qSqvqB\nJHdu2ffZJM+oqidV1WMym576i0WDrW1uLqfiBgDYrapayzfPokqSS5Ocm+S07j5UVS9P8sbMypkb\nuvu6ReMJOADA5JiiAgAmR8ABACZHwAEAJmfUp4nvxk6XdmbcquoT+ea1Db7Q3Zet8njYWVW9IMmb\nuvvFVfX0JG9LspHkU0l+rrst7BuxbT+/s5O8J8nn5ruv6+4/Wt3RwYlz0gecbLm08/wX983zbYxc\nVT0uSbr7xas+Fnanql6f5CeSfHW+6dokV3f37VV1XZIfTvLuVR0fiz3Cz+/cJNd297WrOypYjilM\nUS26tDPj9pwkT6iqW6vqA/OAyrjdneRV+eZFwM7p7tvnj/80yb9cyVGxW9t/fucmeVlV/VlVXV9V\np63u0ODEmkLAecRLO6/qYDguDyS5prtfmuSKJG/3sxu37n5nZnfyPWrr1U6/mh0unc5qPcLP72NJ\nfrG7L0jyhSS/spIDgyWYwj8miy7tzLjdleTtSdLdn0vyt0m+a6VHxPHa+rt2IMnfrepA+Ja8q7uP\n3pfj3UnOXuXBwIk0hYCz6NLOjNulma2ZSlV9d2Zt3L0rPSKO1x1VdcH88Q8muX3RixmdW6rq+fPH\nL0ny8VUeDJxIU1hk/K4kF1XVR+fPL13lwXBcbkjyO1V19B/FS7VvJ42jZ0r9QpJD83vDfCbJO1Z3\nSByHoz+/K5L8VlUdyez/XFy+ukOCE8utGgCAyZnCFBUAwICAAwBMjoADAEyOgAMATI6AAwBMjoAD\nAEyOgAMATI6AAwBMzhSuZAxsUVV3JvnR7v5sVb09yeHu/tn5rUzekNntTX48ycNJ3pfk9Um+P7N7\nEX0+yT/N7JL9H0rymiRPSvLK+XjPT3Jtkick+ZskB7v7nqr6UGY3bvznSb49yb/t7lv25hMD/EMa\nHJiemzO7r1CSPDvJi+aPfzDJe5NcnOSczG6s+PTMLtefzILNf0hSSZ6f5Knd/cIkNyW5vKr2J7k+\nyau7+9zMgs6h+fduJtk/f/2VSX51aZ8OYBcEHJiem5O8pKrOSvKpJA9X1bdnFnCel+QPuvvr3f1w\nkhszC0ObSf5vd/9Vd28m+d9JPjAf739m1uI8M8k/TvKeqrojyZuSPG3L+x5tbD6d5MnL/IAAOzFF\nBdPzF0mem+RfZjbN9P+S/Jsk+5P8XZK1La9dzzf/Dnxj2zgPzf979PX7knyhu89OkqpaT/KdW17/\n9/P/bm57D4A9p8GBiZk3Mx9L8vNJbkvywSS/lFmz88Ekr66qx1XVtyW5dL5tNz6b5MlVdd78+U8l\nefuJPHaAE0XAgWm6OckTuvuuJLdntvD3vd19c2brcD6e2fTV/0jynzJrXDaPMdZmks3u/kZmTdCb\nq+qvkvxkZiHnWN8DsDJrm5v+DgEA06LBAQAmR8ABACZHwAEAJkfAAQAmR8ABACZHwAEAJkfAAQAm\nR8ABACbn/wNAxb09e3FAYgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e59d908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_joint(prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a little more interesting, the objective has been cut in half and we have full support about the men distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EcU7n+B7gl4A1Bl3oZeDeMcZHZFybJM3EqBNtWEwdPObOEC1JdzbOhYX/Cbgd\neBDwUeBK4O1ZFiVJs7Tfia47zpFy4YokHW2cEL00XLzyTgZz0o8DfiTTqiRphlodxzku5sIVSTra\nOCF6O4SwCnwSeEiMcQe4a7ZlSdLseGHhnblwRZKOduxMNPBHwFuBnwM+EEJ4DPDlTKuSpBna3O5S\nX61SWx6nr1AO6Q8Um3aiJemSjv2OEWN8BfD4GOM54GrgD4CfyrowSZqVVmfXeeiLOBMtSUcb53SO\nGvDEEMKjgD3gvwLtrAuTpFlIkoStdpe73u1M3qXMFWeiJelo44xzvILBmu8bGXSunwTcH/jl7MqS\npNno7OzR6yfOQ18kPdbOTrQkXdo4IfrvxRgfmN4JIbwF+Hh2JUnS7KQhcd2TOS5QW16ivlo1REvS\nIca5iuarIYSrDty/G/C1jOqRpJlyW+HhmvUVWh3HOSTpUg7tRA87zgBXAB8PIbybwUz0I4G/yr40\nScre/vF2Xlh4J81GjW989TxJklCpVPIuR5LmylHjHNdfdD8Z/vr7B25L0kJLF61srNmJvlizsUKv\nn9DZ2aNxxj8fSTro0BAdY3xfejuE8KPAo4bv/54Y45uzL02Ssre57aKVw6QjLpvtriFaki5y7Ex0\nCOHZwAuAzwN/DTw3hPDcrAuTpFlwJvpwHnMnSYcb53SOJwJ/N8bYAQghvAr4CPAbWRYmSbOQXjjn\nTPSduXBFkg43zukcFeD8gfvnAV9RJRWCnejDjUK0nWhJutg4nej3AG8IIdzIIFA/afiYJC28VnuX\n1VqVlVo171Lmzmicw76JJF1snBD9DOB/A36eQef6PcAfZFmUJM1Kq921C30Ixzkk6XDjhOh3xhh/\nmMHRdpJUGEmS0Gp3udeVa3mXMpfSOXEXrkjSnY0zE10PIXxH5pVI0oyd3+2x1+t7vN0h7ERL0uHG\n6USfBT4XQvga0Bk+lsQYvyu7siQpe/vbCh3nuKSVWpXVlSqtbTvRknSxcUL0Pxr+mm4pdPerpEIY\nncxhJ/owzXptf6ujJGlknBD9ZeA64B8Ce8DbgD/MsihJmgWPtztes7HCF77WIkkSKhV7KJKUGidE\n/yFwBngVUGVwSsf9GZzaIUkLa3+cw0Urh2o2auz1Es7v9qivjvMtQ5LKYZxXxL8L3DfGmACEEP4c\n+KtMq5KkGUjHFOxEH+7gwhVDtCSNjHM6xxeBgxcRXslgxEOSFtrowkI70Ydx4YokXdq4bYWPhRD+\nG4OZ6GsJPPF2AAAV/ElEQVSAL4UQ3s7glI4fvdQHhBBqwGuAq4BV4EXAbcCNQB/4BHBd2uGWpFlz\nJvp4HnMnSZc2Toh+0UX3X3Hg9lEB+FrgXIzxiSGEy4GPAbcAz4kx3hxCeCXwOOBNkxQsSdOSBsMN\nO9GH2tjvRHvMnSQddGyIjjG+74Sf+78AbxjeXgK6wINjjDcPH3s78MMYoiXlpNXeZWV5idWVat6l\nzK39TrTH3EnSBTK7SiTGuA0QQmgyCNTPA1564F22gMvG+VxnzzanXp80DT43F9v2zh6XNVcL+/c4\njd/XvTp7AOwlPt81PT6XVASZXmodQrgX8GfA78UY/2MI4bcPvLkJfGucz3PuXCuL8qRTOXu26XNz\nwd3R2uHud10r5N/jtJ6fvZ1BB/pvvr5dyD8nzZ6vnZpXk/5wN87pHCcSQvh24F3As2OMNw4fviWE\ncPXw9mOAmy/1sZKUtZ3dHrt7fS8qPMb+6RwdZ6Il6aAsO9HPYTCu8fwQwvOHjz0DeHkIYQW4ldHM\ntCTNlItWxrO6UmVlecnTOSTpIlnORD+DS281fGRWX1OSxuWilfE1GzW2PJ1Dki6Q2TiHJM2z0aIV\nQ/Rx1hsrdqIl6SKGaEmlNFq04jjHcZqNGrt7fXZ2e3mXIklzwxAtqZRctDI+F65I0p0ZoiWV0qbj\nHGNL/4w2HemQpH2GaEml5Ez0+Jp2oiXpTgzRkkrJmejxNevD1d92oiVpnyFaUim12l2WqxXOrFTz\nLmXuuXBFku7MEC2plFrtXZqNFSqVSt6lzL105MVOtCSNGKIllVKr090fU9DRRiHaTrQkpQzRkkqn\nu9djZ7fnRYVjGl1YaCdaklKGaEmls39R4ZoXFY7jzEqV5eqSIVqSDjBESyqd/TOi64bocVQqFZqN\nmuMcknSAIVpS6YyOt3OcY1yDEG0nWpJShmhJpeOilck1GyvsdHvsdnt5lyJJc8EQLal0XLQyOY+5\nk6QLGaIllY7jHJNL58dduCJJA4ZoSaUzGuewEz0uO9GSdCFDtKTSsRM9OReuSNKFDNGSSqfV2aW6\nVKGxupx3KQtjw4UrknQBQ7Sk0mm1u6w3alQqlbxLWRhuLZSkCxmiJZVOq73ropUJpeMcm45zSBJg\niJZUMt29Pp2dnvPQE0r/vLbsREsSYIiWVDJbHS8qPIn66jLVpYoXFkrSkCFaUql4vN3JVCoV1l39\nLUn7DNGSSsXj7U6uWV9x2YokDRmiJZWKneiTazZqdHZ6dPf6eZciSbkzREsqlf1OdN1O9KT2Ly7s\nONIhSYZoSaWSjiNsrNmJntRo4YojHZJkiJZUKpvbzkSflGdFS9KIIVpSqTgTfXJuLZSkEUO0pFJp\ndbosVSo0ziznXcrCSTvRhmhJMkRLKplWu8t6fZmlSiXvUhZO05loSdpniJZUKlvtXUc5TshOtCSN\nGKIllcZer8/2+T0vKjwhO9GSNGKIllQa28PzjdftRJ9I48xgDKblOdGSZIiWVB7pGMKGnegTWapU\nWG/UHOeQJAzRkkpk0+PtTq3ZqNHadpxDkgzRkkpjf+W3negTa9ZrtHf22Ov18y5FknJliJZUGi5a\nOb30z27LuWhJJWeIllQa+53oup3ok/KYO0kaMERLKo30VAnHOU7OY+4kacAQLak0HOc4PTvRkjRg\niJZUGq12lwqw7jjHidmJlqQBQ7Sk0mi1d1mr11haquRdysLasBMtSYAhWlKJtNpd56FPKd326NZC\nSWVniJZUCv1+wnan6zz0Ke3PRLtwRVLJGaIllcJWp0uCJ3Oc1vqZGhWciZYkQ7SkUvBkjulYWqqw\nVq85ziGp9AzRkkrBRSvT02zUvLBQUukZoiWVgotWpqfZWGG706XfT/IuRZJyY4iWVAqOc0xPs1Ej\nYTBnLkllZYiWVAr74xx2ok/NhSuSZIiWVBJp4NuwE31qLlyRJEO0pJLYtBM9NWknetNOtKQSM0RL\nKoWtYeBb83SOU2vaiZYkQ7Skcmi1u6ydWWa56sveaaXHBDoTLanM/G4iqRRa7V3WnYeeiv0LCz2d\nQ1KJGaIlFV4/Sdjq7DkPPSWOc0iSIVpSCbTP79FPErcVTkk6V77lOIekEjNESyo8F61M13J1ibUz\ny3aiJZWaIVpS4aVhb2PNTvS0NBsrXlgoqdQM0ZIKb3N72Imu24melmajRqvTpZ8keZciSbkwREsq\nvPQUCS8snJ5mY4UkgW1P6JBUUoZoSYXnTPT0eUKHpLIzREsqvJYrv6duFKKdi5ZUToZoSYVnJ3r6\n0vlyO9GSysoQLanw0qC37jnRU7PfiXYmWlJJGaIlFV6r3aW+WqW27EvetOyv/nacQ1JJ+R1FUuG1\nOruOckyZFxZKKjtDtKRCS5KErXbXiwqnzE60pLIzREsqtPbOHr1+4qKVKbMTLansDNGSCs3j7bKx\nXF2ivrpsJ1pSaRmiJRWax9tlp9mo2YmWVFrLWX+BEMIPAi+OMV4TQvhu4EagD3wCuC7GmGRdg6Ty\nshOdnWajxjfuOE+SJFQqlbzLkaSZyrQTHUJ4NnADsDp86GXAc2KMjwAqwOOy/PqSNOpEG6KnrVlf\noddPaO/s5V2KJM1c1uMcnwYezyAwAzw4xnjz8PbbgUdn/PUlldyoE+04x7R5caGkMss0RMcY/ww4\n2KI4+O99W8BlWX59SXKcIzsecyepzDKfib5I/8DtJvCtcT7o7NlmNtVIp+Rzc/51+4PLLu59zys4\ne3k952pmK+vn592vHHz+yvKy/y9oIj5fVASzDtG3hBCujjG+H3gM8O5xPujcuVa2VUkncPZs0+fm\nAjj3zW0Auud3OHeuPLO7s3h+LvUHfZEvfvUOzt1tPdOvpeLwtVPzatIf7mYVotMTOJ4J3BBCWAFu\nBd4wo68vqaRa7S6rK1Vqy9W8SykcZ6IllVnmITrG+DngYcPbnwIemfXXlKRUq9OlWXceOgvOREsq\nM5etSCqsJElotXc9mSMjaSd6y060pBIyREsqrPO7PfZ6iSdzZGQ0zmEnWlL5GKIlFZaLVrJVW66y\nulJ1JlpSKRmiJRWWi1ay16zXaHUM0ZLKxxAtqbDSEL1hiM7MxtoKrfYuSZIc/86SVCCGaEmFtek4\nR+aa9Rp7vYTOTi/vUiRppgzRkgrLmejs7R9z1/HiQknlYoiWVFjORGfPhSuSysoQLamw9kO0y1Yy\n48IVSWVliJZUWOmIgZ3o7NiJllRWhmhJhdVqd1lZXmJ1pZp3KYXlwhVJZWWIllRYW+1dLyrM2Gic\nw060pHIxREsqrFa76yhHxhznkFRWhmhJhbSz22N3r2+IzphH3EkqK0O0pEJy0cpsrNaqrNSWaG3b\niZZULoZoSYU0OiPaEJ21Zn3FTrSk0jFESyqk0bZCxzmy1mzUaLW7JEmSdymSNDOGaEmF5KKV2Wk2\nVuju9dnp9vIuRZJmxhAtqZBctDI7ntAhqYwM0ZIKyZno2TFESyojQ7SkQmp5OsfMjBaueHGhpPIw\nREsqpFEn2nGOrNmJllRGhmhJhdRq77JcXeLMSjXvUgrPTrSkMjJESyqkwcrvGpVKJe9SCs9OtKQy\nMkRLKqQ0RCt7dqIllZEhWlLh7HZ77HR7zkPPSHoWd6tjJ1pSeRiiJRWOx9vN1pmVKsvVJTvRkkrF\nEC2pcPYXrdTtRM9CpVLZX/0tSWVhiJZUOHaiZ88QLalsDNGSCicdK9hYsxM9KxuNFXaGs+iSVAaG\naEmFs7k97ETX7UTPyuiYO+eiJZWDIVpS4ezPRHs6x8yMjrlzpENSORiiJRWOM9Gz58IVSWVjiJZU\nOFuG6Jlz4YqksjFESyqcVnuX6lKF+upy3qWUxv7CFTvRkkrCEC2pcFrtLuuNGpVKJe9SSmO/E92x\nEy2pHAzRkgqn1dl10cqMORMtqWwM0ZIKpbvXp7PTY2PNeehZSjvRW4ZoSSVhiJZUKFud9KJCO9Gz\nVF+tUl2qeGGhpNIwREsqlM3t4RnRLlqZqUqlQrNRY9MQLakkDNGSCmW0aMUQPWvNxooz0ZJKwxAt\nqVBGi1Yc55i1ZqPG+d0e3b1+3qVIUuYM0ZIKxW2F+XHhiqQyMURLKpQ0wNmJnj0XrkgqE0O0pEKx\nE52f/bOiXbgiqQQM0ZIKxU50fkbjHHaiJRWfIVpSobQ6XZYqFRpnlvMupXQM0ZLKxBAtqVBa27us\nN2osVSp5l1I6o9XfjnNIKj5DtKRCabW7zkPnxBAtqUwM0ZIKY6/Xp72z57bCnDjOIalMDNGSCmOr\n46KVPDXOLLNUqRiiJZWCIVpSYXi8Xb6WKhXWGzXHOSSVgiFaUmF4vF3+mo2anWhJpWCIllQYdqLz\n16zXaO/ssdfr512KJGXKEC2pMNJO9Iad6NxsrA3+7NP5dEkqKkO0pMLYtBOdu2Z9EKI3t52LllRs\nhmhJhbE17ESv24nOzf5Z0XaiJRWcIVpSYTgTnT8XrkgqC0O0pMJotXepAOtnDNF5ceGKpLIwREsq\njFany1q9xtJSJe9SSmvUiTZESyo2Q7Skwmi1u45y5CydR99ynENSwRmiJRVCv5+w3em6aCVndqIl\nlYUhWlIhbHW6JMCGnehcrZ+pUal4YaGk4jNESyoEV37Ph6WlCuv1mkfcSSo8Q7SkQnDRyvxoNlZc\ntiKp8AzRkgrBTvT8aNZrbJ/fo9fv512KJGXGEC2pEFy0Mj/Sv4Otzl7OlUhSdgzRkgphvxNdN0Tn\nbbRwxZEOScVliJZUCOmFbI5z5M9j7iSVgSFaUiE4zjE/7ERLKgNDtKRCSDfkrTnOkTs70ZLKwBAt\nqRBa7S5rZ5ZZrvqyljc70ZLKwO82kgphs73rPPScsBMtqQyWZ/0FQwhLwO8DDwR2gF+IMX5m1nVI\nKo5+krDV6XK3Kxp5lyLsREsqh5mHaOAngZUY48NCCD8IXD987JJ+4llv5r5XXc6zfvZBMysw9dKb\nbuG2z90OwH3vnU8N81LHPNQwL3Xs11Aht+fmBXUwB38WOdYA8Nt/cgtJAp/64h289KZbcqtDA6/6\n878C4EPxXK5/H/Pw/LSGS9SR42vn3P1Z5FjHPNQwT3WcRCVJkpl+wRDC9cAHY4z/eXj/izHGex72\n/o995psTgMvWVnjSYwL3PLs+kzpveMutfOqLd1zw2KxrmJc65qGGealjHmqYlzrmoYbD6ri8ucrT\nf/qBXHW35szqmDdnzzY5d64186/70ptu4dbhN8TUvDwvyvj/yDzUMC91zEMN81LHPNRwWB15vn6f\nPdusTPL+eYToG4A/jTG+Y3j/88B3xhgvuR82DdGSNInLm6tcf93D8y4jN3mF6H/x4vfgi7ak08jr\n9XvSEJ3HOMcmcPDHi6XDAvQlfOkt1z/u0K71ND32mW/uA5f6w5xZDfNSxzzUMC91zEMN81LHPNRw\nVB23t3a+dPZsc2Z1zKOzZ2ffyUlgrp8Xs6zDGuarjnmoYV7qmIcajqpjUV6/8+hEPx54bIzxKSGE\nhwL/R4zxx2ZahCRJknQKeXSi3wj8UAjhL4b3n5JDDZIkSdKJzbwTLUmSJC06l61IkiRJEzJES5Ik\nSRMyREuSJEkTMkRLkiRJE8rjdI5jhRCWgN8HHgjsAL8QY/xMvlVJIyGEjwDpmqXPxhj/RZ71SCGE\nHwReHGO8JoTw3cCNDM5s/gRwXYzRq8iVi4uemw8C3gJ8avjmV6YbjKVZCiHUgNcAVwGrwIuA25jg\ntXMuQzTwk8BKjPFhw//5rh8+JuUuhHAGIMZ4Td61SAAhhGcDTwC2hg+9DHhOjPHmEMIrgccBb8qr\nPpXXJZ6bDwFeFmN8WX5VSQBcC5yLMT4xhHA58DHgFiZ47ZzXcY6HA+8AiDF+EPg7+ZYjXeD7gEYI\n4Z0hhHcPf9CT8vRp4PGMNn89OMZ48/D224FH51KVdOfn5kOAHwshvD+E8IchhPX8SlPJ/Rfg+cPb\nS0CXCV875zVEbzBYD57qDUc8pHmwDbwkxvgjwNOAP/b5qTzFGP8M2Dvw0ME1ulvAZbOtSBq4xHPz\ng8CzYoxXA58FXpBLYSq9GON2jHErhNBkEKifx4W5+NjXznn9xr8JNA/cX4ox9vMqRrrIJ4E/Bogx\nfgr4BnD3XCuSLnTw9bIJfCuvQqSLvDHGeMvw9puAB+VZjMothHAv4D3A62OM/5EJXzvnNUT/BfCj\nACGEhwIfz7cc6QJPYTCnTwjhHgz+5eQruVYkXeiWEMLVw9uPAW4+6p2lGXpHCOEHhrcfBXwoz2JU\nXiGEbwfeBTw7xnjj8OGJXjvn9cLCNwI/FEL4i+H9p+RZjHSRVwOvDSGk/3M9xX8p0ZxIryJ/JnBD\nCGEFuBV4Q34lScDoufk04PdCCF0GzYf/Nb+SVHLPYTCu8fwQQjob/Qzg5eO+dlaSxFOPJEmSpEnM\n6ziHJEmSNLcM0ZIkSdKEDNGSJEnShAzRkiRJ0oQM0ZIkSdKEDNGSJEnShAzRkjQjIYSHhBBuOOLt\njw0h/Moxn+PJIYTXDm9/LoRw1fDjXjjteiVJh5vXZSuSVDgxxg8Dv3jEuzyE0VKKwyQH3icBkhjj\nW4C3nL5CSdK4DNGSNCMhhEcC/4ZB+P0fwD8AzgL/Cvg8g21uSQjhc8CfAr8H3A+oAv82xngTUBn+\nl6qEEJ4MXB1jfMrwa7wc2AM+ANw3xnhNCOG7gd8H7gK0gX8VY/xoCOFG4FsMAvw9gRfGGG8MIVzB\nYDtnAHaAX40xvjeE8I+AFwI14K+BX4wxfnOqf1CStAAc55Ck2TnYRa7FGB8G/ArwohjjbcArgVfG\nGF8HPA/4UIzx7wBXA88NIXznUZ83hLAM/Afg52KMDwZ2D3y91wHPjjE+BHgqcNOBj79njPEfAI8F\nXjp87NeBT8YYvxd4IvAbIYS7Ar8F/PDw878L+Len+POQpIVlJ1qS8vGO4a9/BVwxvH2ww/xooB5C\n+OfD+w0GXenDxj0qwAOAv4kxfmL42GuA3w0hrAE/ALw2hJC+/9qw25wwCMMX1/II4J8BDD/fw0II\nPw58B/C+4eepAt+Y4PcsSYVhiJakfOwMf024MDynIXkJuDbG+FGAEMLdGATWa4/4nD0u/BfG9PNW\ngU6M8UHpG0II94oxfnMYhncAYozJgZDdPVhXCOG+w8/932OMjxs+dgZojvOblaSicZxDkmancszb\nuwxmjQHeA/wSQAjh7sAtwL2O+by3AZeHEO4/vP9zQD/GuAl8KoRw7fDz/RDwvmNquRn42eH7fw/w\nNgZz3H8vhHCf4fs8D/jtYz6PJBWSIVqSZueCUzUu8fjNwLUhhOsYXLxXDyH8P8C7Gcwzf/aQj01P\n6egCTwBeH0L4EIMLBc8P3+9a4BdCCB8DfgP4mUt8/YO3XwDcJ4TwUeCPgCfEGL8K/HPgP4cQPg48\nCPjVyf8YJGnxVZLkuNOUJEmLIIRQAV7M4ISNdgjhV4G7xxh/LefSJKlw7ERLUkHEGBPgm8D/DCHc\nAvx94DfzrUqSislOtCRJkjQhO9GSJEnShAzRkiRJ0oQM0ZIkSdKEDNGSJEnShAzRkiRJ0oT+fxbE\n8GVLmxmxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e992860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_marginal(prob_women)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAswAAAHrCAYAAADbkMsJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nawAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e9c1160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_marginal(prob_men)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see here that the men's marginal distribution is flat."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.86710996372576221"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Furthermore, the joint probability is of course not perfectly correlated, although it is still highly correlated.\n",
    "At this point it may be fair to say we have found a contradiction.\n",
    "Let's continue anyway with a few more constraints.\n",
    "I think it's fair to have the marginal distributions be the same and not just the average, so let's add that constraint."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "constraints.append(prob_women == prob_men)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'optimal'"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "problem = cvx.Problem(objective, constraints)\n",
    "problem.solve()\n",
    "problem.status"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3237944074262487e-10"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "objective.value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Okay this is effectively zero.\n",
    "So with the added constraint the expected intelligence of a bright women's husband is the same as her own."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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baXyO1Vr/Y/MjAQBmwtATnztKKT+e5PYkj51cWWv9P82OCgCggY00Pm/M8tDWT6xY/7yn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\nAIOh8QEABuP/A3ZB7gx6o5G2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e9b9e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_joint(prob)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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D1WGWgLFtm7W5h5n/wXZKy2vonprErIkD6Nstxa+fV6dEnEq5Kc1VW+fl/Q37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\nMwAADAhmAAAYEMwAADAgmAEAYOD/AVU/UvmWexxBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e905128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_marginal(prob_women)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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D1WGWgLFtm7W5h5n/wXZKy2vonprErIkD6Nstxa+fV6dEnEq5Kc1VW+fl/Q37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\nMwAADAhmAAAYEMwAADAgmAEAYOD/AVU/UvmWexxBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e154b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_marginal(prob_men)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.75440080814813226"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This also violates Kahneman's \"regression to the mean\" since we have a joint distribution that is not perfectly correlated yet bright women are just as smart as their husbands on average."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the wikipedia page on [regression to the mean](https://en.wikipedia.org/wiki/Regression_toward_the_mean) the definition is more restrictive.\n",
    "It states that for a bivariate distribution to exhibit regression to the mean the following must hold,\n",
    "\n",
    "$$\\mu \\le E[X_2 | X_1 = c] < c$$\n",
    "\n",
    "where $\\mu$ is the mean value and the opposite inequalities hold when $c < \\mu$.\n",
    "This would be easier to violate than the current objective because only one inequality needs to be violated i.e. one $c$ to not satisfy regression to the mean.\n",
    "For fun though, I'll try to violate them all by adding those as constraints."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "constraints.extend([(np.arange(N) * prob[:, i]) >= cvx.sum_entries(i * prob[:, i]) for i in range(N//2, N)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And also to below average intelligence women."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "constraints.extend([(np.arange(N) * prob[:, i]) <= cvx.sum_entries(i * prob[:, i]) for i in range(N//2)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'optimal'"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "problem = cvx.Problem(objective, constraints)\n",
    "problem.solve()\n",
    "problem.status"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.332818300170402e-10"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "objective.value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again this is zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAj0AAAHrCAYAAAAkHiyuAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBaEHABgFoQcAGIX/D/WmPyAd7lYsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e934fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_joint(prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we see that this effectively makes the joint probability perfectly correlated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0UnBjAYg0juPosVd2Sho8OYwTwhAoX1qCLj51upraevTS+3vcjgMAARXob0va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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef536d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_marginal(prob_women)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99999999987333121"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we see what happens when we try to make *every* married husband **not** regress to the mean.\n",
    "It is an impossibility and we end up with a perfectly correlated distribution.\n",
    "And I can check that the last 20 inequality constraints are in fact equivalent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "difference = [((np.arange(N) * prob[:, i]) -\n",
    "               cvx.sum_entries(i * prob[:, i])).value for i in range(N)]\n",
    "np.allclose(difference, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*This blog post was written entirely in the [IPython](http://ipython.org) Notebook.\n",
    "The full notebook can be downloaded [here](https://raw.githubusercontent.com/jwkvam/jwkvam.github.io/master/notebooks/kahneman_regression.ipynb) or viewed statically [here](http://nbviewer.ipython.org/url/jwkvam.github.io/notebooks/kahneman_regression.ipynb).\n",
    "You can find me on [GitHub](https://github.com/jwkvam), [LinkedIn](https://linkedin.com/in/jwkvam) and [Twitter](https://twitter.com/jwkvam).*\n"
   ]
  }
 ],
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