CS369-A2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# COMPSCI 369 - Assignment 2\n",
    "\n",
    "- **Sabaoon Raza Khan**\n",
    "- skha787@aucklanduni.ac.nz\n",
    "- 983957824\n",
    "<br>\n",
    "\n",
    "### Problem 1: Pseudoinverse\n",
    "\n",
    "#### Part (a)\n",
    "For the grayscale image, forming a pseudoinverse matrix Pinv. <br>\n",
    "Illustrating the obtained results by displaying Pinv, A and I as images \n",
    "(linearly scaling Pinv and I to the range [0,255] before displaying them)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "P_inv =\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASoAAAD8CAYAAADAKumpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19abc2a6588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "A =\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOEAAAD8CAYAAACB+8M/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19aba12d780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "I =\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19abc747940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Importing necessary packages\n",
    "from matplotlib import pyplot\n",
    "import re\n",
    "import numpy\n",
    "import numpy.linalg\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def read_pgm(filename, byteorder='>'):\n",
    "    \"\"\"Return image data from a raw PGM file as numpy array.\n",
    "\n",
    "    Format specification: http://netpbm.sourceforge.net/doc/pgm.html\n",
    "\n",
    "    \"\"\"\n",
    "    with open(filename, 'rb') as f:\n",
    "        buffer = f.read()\n",
    "    try:\n",
    "        header, width, height, maxval = re.search(\n",
    "            b\"(^P5\\s(?:\\s*#.*[\\r\\n])*\"\n",
    "            b\"(\\d+)\\s(?:\\s*#.*[\\r\\n])*\"\n",
    "            b\"(\\d+)\\s(?:\\s*#.*[\\r\\n])*\"\n",
    "            b\"(\\d+)\\s(?:\\s*#.*[\\r\\n]\\s)*)\", buffer).groups()\n",
    "    except AttributeError:\n",
    "        raise ValueError(\"Not a raw PGM file: '%s'\" % filename)\n",
    "    return numpy.frombuffer(buffer,\n",
    "                            dtype='u1' if int(maxval) < 256 else byteorder+'u2',\n",
    "                            count=int(width)*int(height),\n",
    "                            offset=len(header)\n",
    "                            ).reshape((int(height), int(width)))\n",
    "\n",
    "\n",
    "def display_pgm(array):\n",
    "    pyplot.imshow(array, pyplot.cm.gray)\n",
    "    pyplot.axis('off')\n",
    "    pyplot.show()\n",
    "\n",
    "image = read_pgm(\"sabaoon.pgm\")\n",
    "\n",
    "\n",
    "# Creating pseudoinverse starts here -------------------------------------------------------------\n",
    "U, D, Vt = numpy.linalg.svd(image)             # Performing SVD to find Pseudoinverse of image\n",
    "\n",
    "V = numpy.transpose(Vt)\n",
    "Dinv = numpy.diag(D**(-1))                     #Finding diagonal matrix inverse\n",
    "Ut = numpy.transpose(U[: , :100])              #Trimming columns of U to size of image\n",
    "\n",
    "Pinv = numpy.dot(V, numpy.dot(Dinv, Ut))       #Formula to find Pseudoinverse using SVD\n",
    "# Creating pseudoinverse ends here ---------------------------------------------------------------    \n",
    "    \n",
    "    \n",
    "I = numpy.matrix(Pinv) * numpy.matrix(image)   # Approximation to the 100 × 100 identity matrix.\n",
    "\n",
    "\n",
    "# Function to rescale matrix values\n",
    "def rescale(matrix):\n",
    "    height, length = matrix.shape              # Matrix Dimensions\n",
    "    minimum = matrix.min()                     \n",
    "    maximum = matrix.max()\n",
    "    new_matrix = numpy.empty([height, length]) # Creating a new matrix with the same dimensions, so the original isn't changed\n",
    "    for i in range(height):\n",
    "        for j in range(length):\n",
    "            new_matrix[i, j] = 255 * ((matrix[i, j] - minimum) / (maximum - minimum)) # Given rescaling formula\n",
    "    return new_matrix\n",
    "\n",
    "\n",
    "# Displaying images\n",
    "print(\"\\nP_inv =\")\n",
    "display_pgm(rescale(Pinv))\n",
    "\n",
    "print(\"\\nA =\")\n",
    "display_pgm(image)\n",
    "\n",
    "print(\"\\nI =\")\n",
    "display_pgm(rescale(I))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Part (b)\n",
    "Calculating the elementwise error matrix E = I_100 − I between the computed identity I & the actual identity matrix I_100.<br>\n",
    "Displaying the matrix of absolute values of entries of E as an image, linearly scaling before displaying and calculating the range, mean and standard deviation of entries of E."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Eabs =\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19aba33f5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Range of E = ( -1.0304083975e-13 , 1.42005656366e-13 )\n",
      "Mean of E = 9.7210027571e-17\n",
      "Standard Deviation of E = 7.2054715027e-15\n"
     ]
    }
   ],
   "source": [
    "n = 100                                    # Initialising identity matrix size\n",
    "I_100 = numpy.matrix(numpy.identity(n))    # Creating 100 x 100 identity matrix\n",
    "                     \n",
    "#Elementwise Error Matrix\n",
    "E = I_100 - I\n",
    "E_abs = numpy.fabs(E)\n",
    "\n",
    "# For visualisation, linearly mapping values of the matrix elements E_abs to the range [0, 255].\n",
    "Eabs_rescaled = rescale(E_abs)\n",
    "\n",
    "print(\"\\nEabs =\")\n",
    "display_pgm(Eabs_rescaled)\n",
    "\n",
    "print(\"Range of E = (\", E.min(), \",\", E.max(), \")\")\n",
    "print(\"Mean of E =\", E.mean())\n",
    "print(\"Standard Deviation of E =\", E.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<br>\n",
    "### Problem 2: Principal components to find geographic structure\n",
    "#### Part (a & b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1th Principal Component Vector:\n",
      "\n",
      "[[-0.00309649]\n",
      " [ 0.00967343]\n",
      " [ 0.01110168]\n",
      " [-0.02960344]\n",
      " [-0.02029166]]\n",
      "\n",
      "2th Principal Component Vector:\n",
      "\n",
      "[[ 0.0007713 ]\n",
      " [-0.00202   ]\n",
      " [ 0.00341425]\n",
      " [ 0.02310279]\n",
      " [-0.02630384]]\n",
      "\n",
      "3th Principal Component Vector:\n",
      "\n",
      "[[ 0.00668421]\n",
      " [-0.0031567 ]\n",
      " [-0.01207643]\n",
      " [ 0.00512964]\n",
      " [ 0.01816446]]\n",
      "\n",
      "4th Principal Component Vector:\n",
      "\n",
      "[[-0.02467032]\n",
      " [ 0.01048967]\n",
      " [-0.03225923]\n",
      " [ 0.01962407]\n",
      " [ 0.00753193]]\n",
      "\n",
      "5th Principal Component Vector:\n",
      "\n",
      "[[ 0.00117122]\n",
      " [-0.01353448]\n",
      " [ 0.00688643]\n",
      " [-0.01643924]\n",
      " [-0.05100944]]\n",
      "\n",
      "First 100 singular values:\n",
      "\n",
      "[  5.09446651e+00   3.48091903e+00   3.02265366e+00   3.00997976e+00\n",
      "   2.99768948e+00   2.96751093e+00   2.96489665e+00   2.95102145e+00\n",
      "   2.94488698e+00   2.92125537e+00   2.91542627e+00   2.89992617e+00\n",
      "   2.88708559e+00   2.87940308e+00   2.86512274e+00   2.84936443e+00\n",
      "   2.83973889e+00   2.81949451e+00   2.81183830e+00   2.80548121e+00\n",
      "   2.79994663e+00   2.79033285e+00   2.77886006e+00   2.76955064e+00\n",
      "   2.76351703e+00   2.75219383e+00   2.73596245e+00   2.72624946e+00\n",
      "   2.71459131e+00   2.71077654e+00   2.69336838e+00   2.69055102e+00\n",
      "   2.68641180e+00   2.67604878e+00   2.65944238e+00   2.65647146e+00\n",
      "   2.64631737e+00   2.63935594e+00   2.62780139e+00   2.62202879e+00\n",
      "   2.61408332e+00   2.60056065e+00   2.59550494e+00   2.59149560e+00\n",
      "   2.58657188e+00   2.58419338e+00   2.56899351e+00   2.56544379e+00\n",
      "   2.55468549e+00   2.54597893e+00   2.53125706e+00   2.52376256e+00\n",
      "   2.52345737e+00   2.51127936e+00   2.50656745e+00   2.49487750e+00\n",
      "   2.48974430e+00   2.47881615e+00   2.46973765e+00   2.45929143e+00\n",
      "   2.45181123e+00   2.44668022e+00   2.44355269e+00   2.42928565e+00\n",
      "   2.42073084e+00   2.41569797e+00   2.41001469e+00   2.39594099e+00\n",
      "   2.38226985e+00   2.37722700e+00   2.37216951e+00   2.36440773e+00\n",
      "   2.34931960e+00   2.34493487e+00   2.33765720e+00   2.33126330e+00\n",
      "   2.32688412e+00   2.31531220e+00   2.30311012e+00   2.29924321e+00\n",
      "   2.28927288e+00   2.27158938e+00   2.26067251e+00   2.24777559e+00\n",
      "   2.24482331e+00   2.22689904e+00   2.22033391e+00   2.21545103e+00\n",
      "   2.19869929e+00   2.18364868e+00   2.18228178e+00   2.16988426e+00\n",
      "   2.15702106e+00   2.13956869e+00   2.13594285e+00   2.10734186e+00\n",
      "   2.09166331e+00   2.07693100e+00   2.02453705e+00   1.99018246e-15]\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "# Q2(a)\n",
    "# With the help of numpy.linalg.svd, writing code to read in the data matrix \n",
    "# and performing a principal components analysis of it (centering and scaling the matrix as well).\n",
    "\n",
    "# Reading in data from given file\n",
    "read_in = numpy.loadtxt('snps.txt')\n",
    "\n",
    "# Taking transpose of data matrix\n",
    "data = numpy.matrix(numpy.transpose(read_in))\n",
    "m , n = data.shape\n",
    "\n",
    "# Data Matrix centred & scaled:\n",
    "mean = data.mean(axis = 1)\n",
    "A = data - mean                                           # Centering by subtracting mean of matrix from original\n",
    "Y = numpy.dot((1 / math.sqrt(n-1)), numpy.transpose(A))   # Scaling data using formula given in Lecture 8.8\n",
    "\n",
    "# Finding covariance\n",
    "covariance = numpy.dot(numpy.transpose(Y), Y) \n",
    "\n",
    "# Applying SVD to centred and scaled matrix Y\n",
    "U, S, Vt = numpy.linalg.svd(Y)\n",
    "\n",
    "# ------------------------------------------------------------------------------------------------------------------\n",
    "\n",
    "# Q2(b)\n",
    "# i) Printing out the first 5 entries of each of the first 5 principal component vectors.\n",
    "\n",
    "# Columns of V are the principal components of A\n",
    "V = numpy.transpose(Vt)\n",
    "for i in range(1, 6):\n",
    "    pci = V[:5, i-1:i]\n",
    "    print(i, \"th Principal Component Vector:\\n\", sep = \"\")\n",
    "    print(pci)\n",
    "    print()\n",
    "\n",
    "# ii) Printing out the singular values corresponding to each of the 100 principal components in order.    \n",
    "print(\"First 100 singular values:\\n\")\n",
    "print(S[:100])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Part (c)\n",
    "Project each data vector along the first two principal components to get a $100 × 2$\n",
    "matrix $L$ in which entry $Lij$ corresponds to the amount of the $ith$ individual in the\n",
    "direction of the $jth$ principal component. Print out $L$ in your report."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix L =\n",
      "\n",
      "[[-12.25345945  -7.66429527]\n",
      " [-13.31654607  -5.23714412]\n",
      " [-13.37543386  -6.47311786]\n",
      " [-13.42642572   0.3636625 ]\n",
      " [-15.92288863   0.74686909]\n",
      " [-14.68502787  -0.59857039]\n",
      " [-13.81938536  -7.51558499]\n",
      " [-15.15975615   1.45318795]\n",
      " [-15.77602965   0.65129337]\n",
      " [-14.06883483  -5.88993335]\n",
      " [-14.01610033   0.18179319]\n",
      " [ -2.00172653  -0.74173201]\n",
      " [ -1.35411827  -1.3899567 ]\n",
      " [-13.72498617  -6.2981713 ]\n",
      " [ -2.01946814  -2.15120017]\n",
      " [-14.17543562   1.3568976 ]\n",
      " [-13.36615439  -0.09546892]\n",
      " [-14.2147831    2.02240075]\n",
      " [ -2.15193829  -0.43390261]\n",
      " [-13.9484748    0.19928523]\n",
      " [-14.66870428  -0.64094981]\n",
      " [ -1.71200916  -2.72280705]\n",
      " [-14.34130585   2.26695624]\n",
      " [-11.96829961  -8.14189593]\n",
      " [-14.91098254  -0.06427109]\n",
      " [-13.55784888  -4.55324331]\n",
      " [-13.70352075  -7.33297375]\n",
      " [ -1.56403991  -1.75443817]\n",
      " [-14.74362412   1.63828965]\n",
      " [-13.07938751  -6.01307742]\n",
      " [ -1.18860562  -2.26175799]\n",
      " [ -2.35532045  -1.29908707]\n",
      " [-14.84878959   1.16003582]\n",
      " [-13.89933484   1.54630099]\n",
      " [-13.24650597  -7.13675141]\n",
      " [ -1.44452702  -0.43617283]\n",
      " [-13.91432788   0.83857749]\n",
      " [-13.22975552  -7.10393676]\n",
      " [-12.95149783  -6.77268441]\n",
      " [-13.84728701  -7.24131021]\n",
      " [-15.54855289  -0.48014098]\n",
      " [-13.62856983  -8.13565204]\n",
      " [-13.04981635  -6.22777817]\n",
      " [-14.8049511   -0.25357018]\n",
      " [-14.53042279   0.94688642]\n",
      " [-14.56786073   1.28729582]\n",
      " [ -1.56629094  -1.97031132]\n",
      " [-16.3823496    0.78202532]\n",
      " [-12.92211219  -8.16516287]\n",
      " [-13.30482571  -7.5691645 ]\n",
      " [ -1.67262747  -2.31197033]\n",
      " [ -1.30082632  -0.61628999]\n",
      " [-15.21603563  -0.68853252]\n",
      " [-13.21934091  -1.39157659]\n",
      " [ -2.2788598   -0.88643751]\n",
      " [-16.19798447   1.17228542]\n",
      " [-13.39741022  -8.48932145]\n",
      " [-14.05205921   0.79591156]\n",
      " [-14.63965826   2.52415656]\n",
      " [-15.2270695    1.33367685]\n",
      " [-14.01459295  -6.80412795]\n",
      " [-14.23390426   0.8303667 ]\n",
      " [ -1.4750014   -1.9543763 ]\n",
      " [-14.81658985  -2.48592913]\n",
      " [-12.97091527  -7.64445659]\n",
      " [ -1.79158136  -2.64578082]\n",
      " [ -1.69875521  -2.74685752]\n",
      " [-15.1751364    0.42829664]\n",
      " [-13.45445392  -1.23311542]\n",
      " [-13.69717587   2.74914682]\n",
      " [-13.46783027   0.88601077]\n",
      " [-13.54347214  -6.17660328]\n",
      " [-13.24094658  -5.55670139]\n",
      " [-14.78015433   0.46954215]\n",
      " [-13.22309225  -7.02747942]\n",
      " [-14.11897665   2.42066873]\n",
      " [-14.39252814   2.3178696 ]\n",
      " [ -1.78568049  -0.30739721]\n",
      " [-14.09314452  -7.46791551]\n",
      " [-15.65294799  -1.02324362]\n",
      " [-16.0458427   -0.76143479]\n",
      " [-14.5551633   -8.44662889]\n",
      " [-13.10984127  -6.54518317]\n",
      " [-15.55651732  -0.07928285]\n",
      " [-14.77185471   1.07320141]\n",
      " [-14.78484013   0.95077119]\n",
      " [-14.33380527  -8.54104442]\n",
      " [-15.20827034  -0.81722083]\n",
      " [-15.22667251   0.1848578 ]\n",
      " [-13.69068884  -7.27373011]\n",
      " [-14.65107322  -0.11587801]\n",
      " [-13.37657793  -7.53458037]\n",
      " [ -1.35910613  -1.48218772]\n",
      " [-13.96367614  -0.93148799]\n",
      " [-15.26097191  -0.95151365]\n",
      " [ -1.57353515  -1.30723484]\n",
      " [ -1.75990533  -1.35033108]\n",
      " [-14.83494117   2.39131583]\n",
      " [-14.3920027   -6.77375209]\n",
      " [-14.90921092   0.30910221]]\n"
     ]
    }
   ],
   "source": [
    "pc2 = V[:, :2] # First two principal components\n",
    "L = numpy.transpose(data) * pc2\n",
    "print(\"Matrix L =\\n\")\n",
    "print(L)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Part (d)\n",
    "Plot $L$. From your plot, determine the number of distinct subpopulations in the\n",
    "data set and describe a rule for partitioning the space into the different subpopulations.\n",
    "Include a list of the individuals (corresponding to row numbers) in the largest\n",
    "subpopulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEWCAYAAAB42tAoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAG31JREFUeJzt3XuQZGd53/Hvo11pwVxMvFxUIG2Jm4KB5WIGmcGmGLGy\nuMRAiByKlG1BZGuACMdy4VK8liuFi5SFBTaiSqScAQmzCVUUZEFgBBZIMISkRohZkBACHMAGIYSM\npAoBAqzYnSd/nG5Pq9V9+jLdfd6Z/n6qpnq6+/TMU7O959fv9URmIklSPyc0XYAkqWwGhSSplkEh\nSaplUEiSahkUkqRaBoUkqZZBIc1ARCxFxG1N1yGNw6CQBoiIb0bEWUMc96qIOB4RP4qIH0TEjRHx\n62P8vr+OiP80XrXS5BkU0mStZeYDgYcAVwDvi4h/1nBN0pYYFNIUZOYGcCVwf+Cx3c9HxC9GxGpE\nfD8ibomIl7QeXwZ+E7io1TL5m5kWLvWwu+kCpJ0oInYDvwv8CPga8PSO504E/oYqSM4GfhX4UEQs\nZOZKRDwbuC0z/2T2lUv3ZYtCmqxnRcT3gTuAfwO8LDP/b/cxwAOBN2XmPZn5SeAjreOl4tiikCbr\n+sz81QHHPBL4dqt7qu1bwKOmV5Y0PlsU0uzdDpwaEZ3///YB32l975bOKopBIQ3nxIi4X8fXVlrj\nnwV+TDVgfWJELAEvBt7bev4fgcdsrVxpcgwKaTgfBX7S8fWGcX9QZt5DFQwvBO4C/jNwbmZ+tXXI\nFcATWzOirtpK0dIkhBcukiTVsUUhSapVbFBExK6I+EJEfKTpWiRpnhUbFMDvA19pughJmndFBkVE\nnAL8C+CdTdciSfOu1AV3lwEXAQ/qd0BrT5xlgAc84AHPeMITnjCj0iRpZzhy5MhdmfmwQccVFxSt\nbZm/l5lHWvPLe8rMFWAFYGFhIdfX12dUoSTtDBHxrWGOK7Hr6VeAl0TEN6kWID0vIv5bsyVJ0vwq\nLigy82BmnpKZpwGvAD6Zmb/VcFmSNLeKCwpJUlmKG6PolJmrwGrDZUjSXLNFIUmqZVBIkmoZFJKk\nWgaFJKmWQSFJqmVQSJJqGRSSpFoGhSSplkEhSaplUEiSahkUkqRaBoUkqZZBMQ/W1uCSS6pbSRpR\n0bvHagLW1uDAAbjnHjjpJLjuOlhcbLoqSduILYqdbnW1Conjx6vb1dWmK5K0zRgUJZtEl9HSUtWS\n2LWrul1amlR1kuaEXU+lmlSX0eJi9drV1Sok7HaSNCKDoiRra5sn9F5dRv1O8p2v63XM4qIBIWls\nBkUpulsQl11W3bbvt7uMukPBwWpJU2ZQlKK7BXH33fftMmqHwtGj1ZjD5ZdXxw3b8pCkMRgUpWgP\nOne2ILq7jFZXq5DY2Ki+LrgA3v723i0PSZoQg6IUwww6Ly1VLYmNjer+xkbvlockTVBkZtM13EdE\nnAocAh4BJLCSmW/rd/zCwkKur6/PqrxmraxULYmNDdizxzEJSWOLiCOZuTDouFJbFMeA12fm5yPi\nQcCRiPhEZn656cIat7wM+/dXLYi9ezcX0BkWkqakyKDIzO8C3219/8OI+ArwKMCggM1QcLaTpBko\nfmV2RJwGPB34bNfjyxGxHhHrd955ZxOlNcutOSTNSNFBEREPBA4DF2bmDzqfy8yVzFzIzIWHPexh\nzRTYJLfmkDQjRXY9AUTEiVQh8Z7M/EDT9RTHrTkkzUiRQRERAVwBfCUz/7Lpeorl1hySZqDUrqdf\nAX4beF5E3Nj6elHTRc2MFxqSVJAiWxSZ+T+BaLqORkxi76ZBmwRK0giKDIq5Nsqusb24SaCkCSu1\n62lnq+ta2upsJqfNSpowWxSzNugT/6izmbq7mXptLihJW2BQzNqhQ/DTn0Jm/66lztlMdeMN/ULH\nabOSJsigmKW1NXjXu6qQgKp7qe4T/6DWR7/xDKfNSpogxyiGManpqqurcOxY9X0EnHfevU/o3b9n\n0HiDq7MlzYAtikEmOYuoe/zg3HPrf8+g8Qa7mSTNgEExyFanq3aqO7F3/p6jR+ENb6i+BgWB3UyS\npsygGGTSs4j6ndjbv6d9qdNrr4XPfKYKioMHt/Y7JWkLDIpBZtW90/49F14In/tcFRad4xJ2L0lq\niEExjFl279x0071nRe3dO/oYyaAtPNziQ9IIDIp+mjiZ9poVdffd/cdIOmtsv37v3qpV0i9Y3OJD\n0ogMil6GOZlOI0j6zYrqNUbSWePu3VUr5PhxOOGE6raz62qYtReS1IdB0cugk2l3kFx2WfXJf6uh\n0W88pNdjnTVubFSPZVZfJ5xQtUh6Db67xYekERkUvQw6mXZPZX3d66qT9SS6cnqNh/R6rLPGzhbF\noOBy7YWkERkUvQw6mXaepCPqu3pmVSMMf/J37YWkEUS2Z9hsYwsLC7m+vj7bX9oeoxg0eDzuz/XT\nvqQpi4gjmbkw6DhbFOPq/FS+f/9oJ/d+YeCMJEkFMigmYZSunLowmOWMJFsukoZkUMxavzBYW4Nb\nb60W2cF0ZyTZcpE0ArcZn7VeW4O3T9zveEc1OH7++eOfvIfZEt3LpUoagS2KJrzyldXtuedWYXDJ\nJZsnboB9+8YLiZWVaqru8eOwZ0//sHEthaQRFBsUEfEC4G3ALuCdmfmmhkvauu4un/bK60mcuNfW\n4IILNrcAOXq0/xiHaykkjaDIoIiIXcDbgV8DbgM+FxEfzswvN1vZFtVdunSrJ+7V1c0V2jD4Mquu\npZA0pFLHKM4Avp6Zf5+Z9wDvBV7acE1bN81Lly4tVd1NJ5xQrdS+/HKDQNJEFNmiAB4FfLvj/m3A\nL3ceEBHLwDLAvn37ZlfZsHpNP+3Xcug3C2mUKazjtEqcIitpCKUGxUCZuQKsQLUyu+Fy7q1u+mmv\nLp9+s5BGncI6qfUcktSh1K6n7wCndtw/pfXY9jDq9NPOLqldu6r1FIcOTXcKq1NkJQ2p1KD4HPD4\niHh0RJwEvAL4cMM1DW/UsYh2t9H551frKN7xDrjyymqsYRrjGePUKGkyhlnrVJgiu54y81hEvA64\nhmp67JWZeUvDZQ1vnPGCxcXNK9y111Ocf361pmIaYwhOkZVmb5t2+RYZFACZ+VHgo03XMbZxpp/2\nusLdNN9ETpGVpqPfRJG6/dwKnlxSbFBse+P8o/spX9r+6loN/RbXFt7SMCimYSv/6H7Kl7a3ulZD\nvw+DhV/LvtTB7O1tEjOKVlbg+c+vbiVtH4MmiiwuwsGD9w6C7tfs3VvUgLctimmo27tpmC6plRV4\n9aur7z/+8ep2eXl69UqanHEns7RfM+mrZk6AQTGqYU70o67A7nb48H3vGxTS9tHZhTzseGX7NZ27\nSRfSDWVQjGKUsYd+K7CPHq0276vb3fWcczZbEu37krafccYrC7wMgEExiq0OOO3du7nD68ZGdb+X\nduvh8OEqJGxNSNtDd+thnHNGgbMfDYpRbDXpv/CFauV1ZrXL69139z92eXm8gCh4Lra0o/VqPYx7\nzihs9qNBMYphkr7fiXptDd71riokoNqeY9JNysLnYks7Wq/Ww8GDxbUOxmFQjKou6etO1O3tOaBq\nVZx33uTfNIXPxZZ2tH6th8JaB+MwKCap7kTda3uOSStwEEyaGwWOLUyKQTFJdSfqWbyJdvAbVdoW\ndkDroZfILOuaP+NYWFjI9fX1psuobJfB5O1Sp6SpiYgjmbkw6DhbFJO2HT5ROOgtTdYoH7y6j90G\nH9oMinnUby+qwt+sUpFG+eDVfexll913uw4o7v+iQTGPusdS9u61hSGNa5TZht3HHj587/uHDsG7\n313c/0V3j51H7UHvN76xur37bq+fLY1rlMsKdx97zjn3vg/V9j7Hj29u81MAWxTzqnssxWm10nhG\nmW3Y69j9+zfv33zzcNv8zJhBIafVSls1yiSW7mM776+uVtv7bGwM3uZnhgwKVbbDbC1pp1tagj17\nimvdGxSS1KTu6bEFtu4NCklqSr+ptYUERFtxs54i4s0R8dWI+GJEfDAiHtJ0TZI0Ff3WNBWmuKAA\nPgE8OTOfAvxv4GDD9UjSdCwtVVNjI6qvW2+tWhmFKS4oMvPjmdnaj5vrgVOarEeSpqp9MbNjx2Bl\npeqKKiwsiguKLucBH2u6CEmais7r1EA1LbbALqhGBrMj4lrg5B5PXZyZH2odczFwDHhPn5+xDCwD\n7Nu3b0qVStIWDNrwr71S++jRzbUTBU2LbStym/GIeBXwauBAZv540PFFbTMuSTD8ZoHtMNm7t1pg\nN8Npsdt2m/GIeAFwEfDcYUJCkoo0aLPAztbGwT5zdgrZgry4oAAuB/YAn4gIgOsz8zXNliRJI6q7\n4uUwrY2CrhtTXFBk5uOarkGStqxulfUwW5OPsn35lBUXFHOvkKampAnot8q6rrUxyjEzYlCUpKCm\npqQpGmZPp4L2fTIoSlJQU1PSlA2zp1Mh+z6VvuBuvoxypSxJ29PaGlxySXGrr+sMbFFExIOBh2Xm\nN7oef0pmfnFqlc2jgpqakqag3b189Gi1dceLXwwXXVT8//XaFkVEvBz4KnA4Im6JiGd2PP3X0yxs\nbi0uVnOqC3/jSBrD6urmKuzjx+Gqq+DMM4tvXQzqevpj4BmZ+TTg3wL/NSJe1nouplqZJO007d1i\nOxW4t1O3QUGxKzO/C5CZNwBnAn8SEf8eKG/vD0kq2eIiXH75vcNiG4xHDhqj+GFEPLY9PpGZ342I\nJeAq4EnTLk6SdpzlZdi/Hw4dqu6fe27xXc2DguK1dHUxZeYPW/sxvXxqVUnSTlbItNdhDep6+n/A\nI3o8fgbVRYUkSTvcoKC4DPhBj8d/0HpOkrTDDQqKR2Tmzd0Pth47bSoVSZKKMigoHlLz3P0nWYgk\nqUyDgmI9Is7vfjAifhc4Mp2SJEklGTTr6ULggxHxm2wGwwJwEvCyvq+SJO0YtUGRmf8IPDsizgSe\n3Hr46sz85NQrkyQVoTYoIuJ+wGuAxwE3A1dk5rFZFCZJKsOgMYp3U3U13Qy8EHjL1CuSJBVl0BjF\nEzNzP0BEXAHcMP2SJEklGdSi+Fn7G7ucJGk+DWpRPDUi2iuzA7h/634AmZkPnmp1kqTG1bYoMnNX\nZj649fWgzNzd8f1UQyIiXh8RGREPnebvkSTVK/Ka2RFxKnA2cGvTtUjSvCsyKIC3AhfhxZEkqXHF\nBUVEvBT4Tmbe1HQtkqTBg9lTERHXAif3eOpiqut0nz3Ez1gGlgH27ds30fokSZsis5zenYjYD1wH\n/Lj10CnA7cAZmXlHv9ctLCzk+vr6DCqUpJ0jIo5k5sKg4xppUfTTus7Fw9v3I+KbwEJm3tVYUZI0\n54obo5AklaWoFkW3zDyt6Rokad7ZopAk1TIo5s3aGlxySXUrSUMouutJE7a2BgcOwD33wEknwXXX\nweJi01VJKpwtinmyulqFxPHj1e3qatMVSdoGDIp5srRUtSR27apul5aarkjSNmDX0zxZXKy6m1ZX\nq5Cw20nSEAyKebO4aEBIGoldT5KkWgaFJKmWQSFJqmVQSJJqGRSSpFoGxbxzSw9JAzg9dp65pYek\nIdiimGdu6SFpCAbFPHNLD0lDsOtpnrmlh6Qh2KKYd4uLcPBg9b2D2pJ6sEUhB7Ul1bJFIQe1JdUy\nKOSgtqRadj3JQW1JtQyKnWJtbWsneq9TIamPIoMiIn4PuAA4DlydmRc1XFLZHIyWNEXFjVFExJnA\nS4GnZuaTgLc0XFL5Jj0Y7f5PkjqU2KJ4LfCmzDwKkJnfa7ie8rUHo9stiq0MRts6kdSluBYFcDrw\nnIj4bER8OiKe2eugiFiOiPWIWL/zzjtnXGJh2oPRb3zj4BP7oNaCU2UldWmkRRER1wIn93jqYqqa\nfgF4FvBM4H0R8ZjMzM4DM3MFWAFYWFjI7h80d4YZjB6mtbC0VE2T3diobp0qK829RoIiM8/q91xE\nvBb4QCsYboiIDeChwJw3G7agPSPq1lvv21roFS4R976VNNdKHKO4CjgT+FREnA6cBNzVbEnbWGcr\nYtcu2N36J+83lrG6CseOQWZ12y9MJM2NEoPiSuDKiPgScA/wyu5uJ42gc8wB4PzzYd++/ustJjkw\nLmlHKC4oMvMe4LearmPH6D7xn3vuZkD0WqTnKm1JXYoLCk1YvxN/v4Htra7wlrTjGBTzoNeMqH7T\nYF1DIalLiesoNAu9dox1DYWkHmxRzKt+XVIOZEvqEjthQtHCwkKur683XcZs1I0hTGJ8ofNngOMV\n0g4WEUcyc2HQcbYotpO6ldWT2qOpPZ7hnk+SWhyj2E7qxhAmPb7geIWkFoNiO6m7ZOmkL2fq5VEl\ntdj1tJ3ULYbb6kK57vENF95JanEwW1VIPPe58LOfwYknwqc/bTBIc2DYwWy7ngSXXlqFBFS3l17a\nbD2SimLX0041yjTX22+vvy9prhkUO1H31uLtLcNPOgk+9an7hsXv/A7ccMO970tSi0GxE3VObd3Y\nqIIC4OhROHTovkGxvFzdHj4M55yzeV+SMCh2js6ups6txWHzWhR1lpcNCEk9GRQ7Qa9V1NddV7Ue\n7rgDrr666no68cTqehSSNAKDYifotYp6aQne/e7NcYpXv/reFy2CzVbI3r1w992ul5DUk0GxE/S6\nfGn3JVD37btvSBw4UI1bbGzACSfAnj333T/KBXfS3DModoJxtgxvB8nGRnV/Y2OzNbLVTQENGGlH\nMSh2iu6r2A3agqPdCulsUXQGSq/urGFO+u46K+04BsVO1usSqJ3PtYOk1xhFr+6sYYwbMJKKZVDM\ns2GDZJQupHEDRlKxiguKiHga8FfA/YBjwL/LzBvqX6WpqAuSute466y0oxQXFMClwJ9m5sci4kWt\n+0vNlqSRjBMwkopV4u6xCTy49f3PA+5QJ0kNKrFFcSFwTUS8hSrInt3roIhYBpYB9u3bN7vqtqtx\np6xOaqqrU2albauRoIiIa4GTezx1MXAA+IPMPBwRLweuAM7qPjAzV4AVqC5cNMVyt79xp6xOaqqr\nU2alba2RrqfMPCszn9zj60PAK4EPtA59P3BGEzXuKL2mrE7zddP6OZIaUeIYxe3Ac1vfPw/4WoO1\n7AztKau7do02ZXXc103r50hqRIljFOcDb4uI3cBPaY1DaAvGnbI6qamuTpmVtrXI3P7d+wsLC7m+\nvt50GdMzrYFgB5iluRYRRzJzYdBxJbYo1KnXQDBs/QTvALOkIRkUpeseCD50aPM6E1s5wbsnk6Qh\nlTiYrU7dA8EwmRlEDjBLGpItitJ1DwTDvVsU457gHWCWNCQHs7cjB6ElTYCD2TuZm+5JmiHHKCRJ\ntQwKSVItg0KSVMugkCTVMigkSbUMCklSLYNCklTLoJAk1TIoJEm1DApJUi2DQpJUy6CQJNUyKCRJ\ntQwKSVItg0KSVMugkCTVaiQoIuJfR8QtEbEREQtdzx2MiK9HxN9FxPObqE+StKmpK9x9CfhXwH/p\nfDAingi8AngS8Ejg2og4PTOPz75ESRI01KLIzK9k5t/1eOqlwHsz82hm/gPwdeCM2VYnSepU2jWz\nHwVc33H/ttZj9xERy8By6+6PIqJX8EzTQ4G7Zvw7h1FqXVBubdY1mlLrgnJrK7Wufz7MQVMLioi4\nFji5x1MXZ+aHtvrzM3MFWNnqzxlXRKxn5sLgI2er1Lqg3NqsazSl1gXl1lZyXcMcN7WgyMyzxnjZ\nd4BTO+6f0npMktSQ0qbHfhh4RUTsiYhHA48Hbmi4Jkmaa01Nj31ZRNwGLAJXR8Q1AJl5C/A+4MvA\n3wIXFDzjqbFurwFKrQvKrc26RlNqXVBubdu6rsjMaRciSdrGSut6kiQVxqCQJNUyKEY0YPuRp0TE\nWuv5myPifiXU1Xp+X0T8KCL+cFY11dUVEb8WEUdaf6cjEfG8EupqPVfMNjIR8bSIuD4iboyI9Ygo\nZgFqRPxeRHy19Xe8tOl6OkXE6yMiI+KhTdfSFhFvbv29vhgRH4yIhzRczwta7/GvR8Qf1R6cmX6N\n8AX8ItUilVVgoePx3cAXgae27u8FdjVdV8fz/x14P/CHhfy9ng48svX9k4HvFFLXE4GbgD3Ao4Fv\nzPLfsUedHwde2Pr+RcBqU7V01XUmcC2wp3X/4U3X1FHbqcA1wLeAhzZdT0ddZwO7W9//OfDnDday\nq/XefgxwUus9/8R+x9uiGFH2337kbOCLmXlT67i7c4YztmrqIiL+JfAPwC2zqqetX12Z+YXMvL11\n9xbg/hGxp+m6KG8bmQQe3Pr+54Hba46dpdcCb8rMowCZ+b2G6+n0VuAiqr9dMTLz45l5rHX3eqp1\nYk05A/h6Zv59Zt4DvJfqvd+TQTE5pwMZEddExOcj4qKmCwKIiAcC/wH406ZrqXEO8Pn2SadhjwK+\n3XG/7zYyM3Ih8OaI+DbwFuBgg7V0Oh14TkR8NiI+HRHPbLoggIh4KVXr9KamaxngPOBjDf7+kd7n\npe31VIQxtx/ZDfwq8Ezgx8B1EXEkM69ruK43AG/NzB9FxKRKmURd7dc+iaoZfnZJdc1SXZ3AAeAP\nMvNwRLwcuAIYZ9eDSde1G/gF4FlU7/n3RcRjstWv0WBdf8wU3kvDGuY9FxEXA8eA98yytq0wKHrI\n8bYfuQ34H5l5F0BEfBT4JWBiQTFmXb8M/EZrsPEhwEZE/DQzL2+4LiLiFOCDwLmZ+Y1J1dM2Zl0z\n30amrs6IOAT8fuvu+4F3TrOWTgPqei3wgVYw3BARG1Qb393ZVF0RsZ9qXOmm1oeiU4DPR8QZmXnH\ntOuqq60tIl4F/DpwYBahWmOk97ldT5NzDbA/In4uInYDz6VaYd6ozHxOZp6WmacBlwF/NsmQGFdr\nxsfVwB9l5v9qup4OpW0jczvVewngecDXGqyl01VUA9pExOlUA6KN7o6amTdn5sM73u+3Ab80q5AY\nJCJeQDV28pLM/HHD5XwOeHxEPDoiTqK6DtCH+x1sUIyoZvuR/wP8JdU/wI1Ufe5XN11X02rqeh3w\nOOA/tqZ+3hgRD2+6rixvG5nzgb+IiJuAP2Nza/2mXQk8JiK+RDUQ+sqGPyFvB5cDDwI+0Xq//1VT\nhbQG1V9H9QH3K8D7Wu/9ntzCQ5JUyxaFJKmWQSFJqmVQSJJqGRSSpFoGhSSplkEhbUFEHG9NdfxS\nRLw/In6u9fjJEfHeiPhGa3fcj7bWGxARfxsR34+IjzRbvTQcg0Lamp9k5tMy88nAPcBroloW/EGq\nnV4fm5nPoNqj6RGt17wZ+O1mypVGZ1BIk/MZqkWEZwI/y8x/WlCVmTdl5mda318H/LCZEqXRGRTS\nBLS2bXkhcDPV9TWONFuRNDkGhbQ194+IG4F14Faq3V2lHcXdY6Wt+UlmPq3zgYi4BfiNhuqRJs4W\nhTR5nwT2RMQ/beAX1fXUn9NgTdLYDAppwlq7qL4MOKs1PfYW4BLgDoCI+AzVtSUORMRtEfH85qqV\nBnP3WElSLVsUkqRaBoUkqZZBIUmqZVBIkmoZFJKkWgaFJKmWQSFJqvX/ASgDVncQ/82zAAAAAElF\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19abd1158d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('L Plot')\n",
    "plt.xlabel(\"PC1\")\n",
    "plt.ylabel(\"PC2\")\n",
    "plt.plot(L[:,0], L[:,1], 'r.')       # x-axis (Column 1) & y-axis (Column 2)\n",
    "plt.axis([-17.5, 0, -10, 4])         # Setting the range for the x and y axes\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As can be seen from the plot, there are 3 different distinct subpopulations in the data set.\n",
    "<br>\n",
    "A rule for partitioning the space for each of the subpopulations would be:<br>\n",
    "- **Subpopulation 1:** $PC1 < -13$ & $PC2 > -3$\n",
    "- **Subpopulation 2:** $PC1 < -11$ & $PC2 < -4$\n",
    "- **Subpopulation 3:** $PC1 > -3$ & $PC2 > -4$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The list of individuals in the largest subpopulation (1):\n",
      "\n",
      "Individual # 4\n",
      "Individual # 5\n",
      "Individual # 6\n",
      "Individual # 8\n",
      "Individual # 9\n",
      "Individual # 11\n",
      "Individual # 16\n",
      "Individual # 17\n",
      "Individual # 18\n",
      "Individual # 20\n",
      "Individual # 21\n",
      "Individual # 23\n",
      "Individual # 25\n",
      "Individual # 29\n",
      "Individual # 33\n",
      "Individual # 34\n",
      "Individual # 37\n",
      "Individual # 41\n",
      "Individual # 44\n",
      "Individual # 45\n",
      "Individual # 46\n",
      "Individual # 48\n",
      "Individual # 53\n",
      "Individual # 54\n",
      "Individual # 56\n",
      "Individual # 58\n",
      "Individual # 59\n",
      "Individual # 60\n",
      "Individual # 62\n",
      "Individual # 64\n",
      "Individual # 68\n",
      "Individual # 69\n",
      "Individual # 70\n",
      "Individual # 71\n",
      "Individual # 74\n",
      "Individual # 76\n",
      "Individual # 77\n",
      "Individual # 80\n",
      "Individual # 81\n",
      "Individual # 84\n",
      "Individual # 85\n",
      "Individual # 86\n",
      "Individual # 88\n",
      "Individual # 89\n",
      "Individual # 91\n",
      "Individual # 94\n",
      "Individual # 95\n",
      "Individual # 98\n",
      "Individual # 100\n"
     ]
    }
   ],
   "source": [
    "print(\"The list of individuals in the largest subpopulation (1):\")\n",
    "print()\n",
    "\n",
    "rows, cols = L.shape\n",
    "for num in range(rows):\n",
    "    if L[num,0] < -13 and L[num,1] > -3:      # Following the rule for space partitioning\n",
    "        print(\"Individual #\", num + 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "### Problem 3: Sampling from some common distributions \n",
    "#### Part i. (a)\n",
    "**Poisson Distribution** --> Parameters: <br>\n",
    "(1 customer/15 minutes = 4 customers/hour)\n",
    "- $λ = 4$\n",
    "\n",
    "#### Part i. (b & c)\n",
    "Creating a histogram of the given distribution, and finding the mean and variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEWCAYAAAB1xKBvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nKgmMiIioksCIiIgq/x+cN/nv19DeugAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19aba3e0240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Mean of sampled data = 3.84333333333\n",
      "Variance of sampled data = 3.91212222222\n",
      "\n",
      "Theoretical mean = 4\n",
      "Theoretical variance = 4\n",
      "\n",
      "Comparing the theoretical mean and variance to each of the sampled results, we get small variations each time we sample.\n",
      "The difference between the theoretical and sampled mean is: 0.156666666667\n",
      "The difference between the theoretical and sampled variance is: 0.0878777777778\n"
     ]
    }
   ],
   "source": [
    "λ = 4   \n",
    "size = 300                                                    # Sample size\n",
    "bin_size = int(math.sqrt(size))                               # Finding bin size from number of samples & converting to integers\n",
    "\n",
    "s = numpy.random.poisson(λ, size)                             # Randomly samplng values for each distribution\n",
    "\n",
    "count, bins, ignored = plt.hist(s, bin_size, normed=True, color='y')     # Creating histogram of sampled values\n",
    "plt.title('Poisson Distribution Histogram')\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.show()\n",
    "\n",
    "ExpVal = numpy.mean(s)                                        # Expected Value / Mean for sampled data\n",
    "Var = numpy.var(s)                                            # Variance for sampled data\n",
    "print()\n",
    "print(\"Mean of sampled data =\", ExpVal)\n",
    "print(\"Variance of sampled data =\", Var)\n",
    "\n",
    "T_mean = λ\n",
    "T_var = λ\n",
    "print()\n",
    "print(\"Theoretical mean =\", T_mean)                           # Theoretical Mean given the parameters\n",
    "print(\"Theoretical variance =\", T_var)                        # Theoretical Variance \"\" \"\" \"\"\n",
    "\n",
    "print()\n",
    "print(\"Comparing the theoretical mean and variance to each of the sampled results, we get small variations each time we sample.\")\n",
    "print(\"The difference between the theoretical and sampled mean is:\", T_mean - ExpVal)\n",
    "print(\"The difference between the theoretical and sampled variance is:\", T_var - Var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Part ii. (a)\n",
    "**Exponential Distribution** --> Parameters: <br>\n",
    "(Death rate for a type of tree is 0.01 per year)\n",
    "- $λ = 0.01$ \n",
    "\n",
    "#### Part ii. (b & c)\n",
    "Creating a histogram of the given distribution, and finding the mean and variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZIAAAEWCAYAAABMoxE0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nbMfaMJsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19abd5e9908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Mean of sampled data = 106.619248505\n",
      "Variance of sampled data = 9818.9356687\n",
      "\n",
      "Theoretical mean = 100.0\n",
      "Theoretical variance = 10000.0\n",
      "\n",
      "Comparing the theoretical mean and variance to each of the sampled results, we get small variations each time we sample.\n",
      "The difference between the theoretical and sampled mean is: -6.61924850481\n",
      "The difference between the theoretical and sampled variance is: 181.064331302\n"
     ]
    }
   ],
   "source": [
    "λ = 0.01\n",
    "size = 150\n",
    "bin_size = int(math.sqrt(size))\n",
    "\n",
    "s = numpy.random.exponential(1/λ, size)                        # Randomly samplng values for each distribution\n",
    "\n",
    "count, bins, ignored = plt.hist(s, bin_size, normed=True, color='purple')      # Creating histogram of sampled values\n",
    "plt.title('Exponential Distribution Histogram')\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.show()\n",
    "\n",
    "ExpVal = numpy.mean(s)                                         # Expected Value\n",
    "Var = numpy.var(s)                                             # Variance\n",
    "print()\n",
    "print(\"Mean of sampled data =\", ExpVal)\n",
    "print(\"Variance of sampled data =\", Var)\n",
    "\n",
    "T_mean = 1 / λ\n",
    "T_var = 1 / (λ**2)\n",
    "print()\n",
    "print(\"Theoretical mean =\", T_mean)\n",
    "print(\"Theoretical variance =\", T_var)\n",
    "\n",
    "print()\n",
    "print(\"Comparing the theoretical mean and variance to each of the sampled results, we get small variations each time we sample.\")\n",
    "print(\"The difference between the theoretical and sampled mean is:\", T_mean - ExpVal)\n",
    "print(\"The difference between the theoretical and sampled variance is:\", T_var - Var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Part iii. (a)\n",
    "**Binomial Distribution** --> Parameters: <br>\n",
    "(On average 75% of the eggs are predated before hatching, so 25% are those that successfully hatch)\n",
    "- $n = 24$\n",
    "- $p = 0.25$\n",
    "\n",
    "#### Part iii. (b & c)\n",
    "Creating a histogram of the given distribution, and finding the mean and variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEWCAYAAAB1xKBvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDElSEwNDktTk/wMg559aO+lcyQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19abd735828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Mean of sampled data = 6.036\n",
      "Variance of sampled data = 4.846704\n",
      "\n",
      "Theoretical mean = 6.0\n",
      "Theoretical variance = 4.5\n",
      "\n",
      "Comparing the theoretical mean and variance to each of the sampled results, we get small variations each time we sample.\n",
      "The difference between the theoretical and sampled mean is: -0.036\n",
      "The difference between the theoretical and sampled variance is: -0.346704\n"
     ]
    }
   ],
   "source": [
    "n, p = 24, 0.25                                               # Number of trials, Probability of each trial\n",
    "q = 1 - p\n",
    "size = 500\n",
    "bin_size = int(math.sqrt(size))\n",
    "\n",
    "s = numpy.random.binomial(n, p, size)                         # Randomly samplng values for each distribution\n",
    "\n",
    "count, bins, ignored = plt.hist(s, bin_size, normed=True, color='darkorange')     # Creating histogram of sampled values\n",
    "plt.title('Binomial Distribution Histogram')\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.show()\n",
    "\n",
    "ExpVal = numpy.mean(s)                                        # Expected Value\n",
    "Var = numpy.var(s)                                            # Variance\n",
    "print()\n",
    "print(\"Mean of sampled data =\", ExpVal)\n",
    "print(\"Variance of sampled data =\", Var)\n",
    "\n",
    "T_mean = n*p\n",
    "T_var = n*p*q\n",
    "print()\n",
    "print(\"Theoretical mean =\", T_mean)\n",
    "print(\"Theoretical variance =\", T_var)\n",
    "\n",
    "print()\n",
    "print(\"Comparing the theoretical mean and variance to each of the sampled results, we get small variations each time we sample.\")\n",
    "print(\"The difference between the theoretical and sampled mean is:\", T_mean - ExpVal)\n",
    "print(\"The difference between the theoretical and sampled variance is:\", T_var - Var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Part iv. (a)\n",
    "**Normal Distribution** --> Parameters: <br>\n",
    "- $μ = 7$\n",
    "- $σ^2 = 1$\n",
    "\n",
    "#### Part iv. (b & c)\n",
    "Creating a histogram of the given distribution, and finding the mean and variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEWCAYAAACJ0YulAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkSPYVqDrLaQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x19ac5598dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Mean of sampled data = 7.01359867621\n",
      "Variance of sampled data = 1.00303247716\n",
      "\n",
      "Theoretical mean = 7\n",
      "Theoretical variance = 1\n",
      "\n",
      "Comparing the theoretical mean and variance to each of the sampled results, we get small variations each time we sample.\n",
      "The difference between the theoretical and sampled mean is: -0.0135986762124\n",
      "The difference between the theoretical and sampled variance is: -0.00303247716227\n"
     ]
    }
   ],
   "source": [
    "μ, σ = 7, 1                                                      # Mean & Standard deviation\n",
    "size = 1000\n",
    "bin_size = int(math.sqrt(size))\n",
    "\n",
    "s = numpy.random.normal(μ, σ, size)                              # Randomly samplng values for each distribution\n",
    "\n",
    "count, bins, ignored = plt.hist(s, bin_size, normed=True, color='darkblue')        # Creating histogram of sampled values\n",
    "\n",
    "# Plotting a curve to show the shape of the graph\n",
    "plt.plot(bins, 1/(σ * numpy.sqrt(2 * numpy.pi)) * numpy.exp( - (bins - μ)**2 / (2 * σ**2) ), linewidth=3, color='lime') \n",
    "plt.title('Normal Distribution Histogram')\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.show()\n",
    "\n",
    "ExpVal = numpy.mean(s)                                           # Expected Value\n",
    "Var = numpy.var(s)                                               # Variance\n",
    "print()\n",
    "print(\"Mean of sampled data =\", ExpVal)\n",
    "print(\"Variance of sampled data =\", Var)\n",
    "\n",
    "T_mean = μ\n",
    "T_var = σ**2\n",
    "print()\n",
    "print(\"Theoretical mean =\", T_mean)\n",
    "print(\"Theoretical variance =\", T_var)\n",
    "\n",
    "print()\n",
    "print(\"Comparing the theoretical mean and variance to each of the sampled results, we get small variations each time we sample.\")\n",
    "print(\"The difference between the theoretical and sampled mean is:\", T_mean - ExpVal)\n",
    "print(\"The difference between the theoretical and sampled variance is:\", T_var - Var)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}