{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# IntroStat Week 4 \n",
    "\n",
    "Welcome to the 4th lecture in IntroStat\n",
    "\n",
    "During the lectures we will present both slides and notebooks. \n",
    "\n",
    "This is the notebook used in the lecture in week 4.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation: Distribution of the sample mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot histogram of 10 random values (normally distributed)\n",
    "\n",
    "# 'True' values in theoretical population\n",
    "mu = 178\n",
    "sigma = 12\n",
    "\n",
    "# size of sample\n",
    "n = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[180.73138515 168.75715052 175.99444844 169.90764524 163.53737264\n",
      " 196.47793848 160.7261311  190.91340526 196.71512198 169.68598845]\n"
     ]
    }
   ],
   "source": [
    "# Draw 10 random numbers\n",
    "x = stats.norm.rvs(mu, sigma, size=n)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "179.08804725335884\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# calculate sample mean and plot\n",
    "x = stats.norm.rvs(mu, sigma, size=n)\n",
    "print(x.mean())\n",
    "\n",
    "# Plot histogram \n",
    "plt.hist(x, density=True)\n",
    "plt.xlim(140,220)\n",
    "plt.ylim(0,0.20)\n",
    "plt.axvline(x.mean(), linestyle='--', color=\"black\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[173.85581785 178.85375747 183.53245237 172.21368282 182.94441809\n",
      " 182.90463353 177.42709101 170.08980932 172.43047936 177.09631324\n",
      " 173.4225958  180.85155415 183.05325216 176.86362154 173.43697527\n",
      " 180.22411913 182.02788731 180.99996767 180.30339842 181.42525722\n",
      " 175.12982301 183.97408141 178.66822767 180.9381601  179.09786212\n",
      " 180.29513772 176.20352658 186.24327106 182.87915657 170.80852407\n",
      " 177.11779412 175.45072253 177.26594494 179.67015918 178.96907857\n",
      " 179.3511099  173.55834101 176.11638171 174.15991454 176.80076866\n",
      " 181.81149706 174.07197412 181.93080085 172.7829334  175.37021513\n",
      " 174.97687355 182.5955381  180.9092784  178.01459223 183.08545607\n",
      " 175.32084665 178.63091107 181.22464019 181.82965528 174.52701088\n",
      " 174.95175701 181.07809733 178.94996421 178.6491596  177.35030435\n",
      " 180.00484782 180.60579862 172.30600109 174.67529389 179.5488106\n",
      " 178.36968533 179.57634634 180.14839682 178.13654719 182.3625652\n",
      " 179.39223489 175.22591135 175.17765224 174.44027079 181.01097042\n",
      " 173.89570597 178.58519818 177.44444017 174.777065   176.33748454\n",
      " 171.4558117  182.36742097 168.80499522 175.56554693 174.30990737\n",
      " 172.8565992  172.74283591 177.75563055 181.97294831 181.43314971\n",
      " 180.71337317 180.72915686 179.45988361 181.94350222 170.37697997\n",
      " 173.52551798 179.09719327 176.57644054 177.67405759 177.25100749]\n"
     ]
    }
   ],
   "source": [
    "# Repeat 100 times and plot histogram of the mean values\n",
    "\n",
    "# Draw (10 x 100) random numbers\n",
    "mat = stats.norm.rvs(mu, sigma, size=(n,100))\n",
    "\n",
    "# Calculate sample mean of each column \n",
    "xbar = mat.mean(axis=0)\n",
    "\n",
    "print(xbar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot histogram of the mean values\n",
    "plt.hist(xbar, density=True, color=\"black\")\n",
    "plt.xlim(140,220)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### t-distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the t-distribution\n",
    "plt.plot(np.arange(-3,3,.01), stats.t.pdf(np.arange(-3,3,.01), df=9), color=\"red\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: find correct quantile in t(9)-distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "height_data = np.array([168, 161, 167, 179, 184, 166, 198, 187, 191, 179])\n",
    "xrange = np.arange(140, 220, .1)\n",
    "plt.hist(height_data, density=True)\n",
    "plt.ylim(0,.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "178.0\n",
      "12.211106056009468\n"
     ]
    }
   ],
   "source": [
    "# calculate mean (xbar) and sample standard deviation (S)\n",
    "xbar = height_data.mean()\n",
    "s = height_data.std(ddof=1)\n",
    "print(xbar)\n",
    "print(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.262157162740992\n"
     ]
    }
   ],
   "source": [
    "t_lower = stats.t.ppf(.025,df=9)\n",
    "print(t_lower)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.2621571627409915\n"
     ]
    }
   ],
   "source": [
    "t_upper = stats.t.ppf(.975,df=9)\n",
    "print(t_upper)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[169.26470095351434, 186.73529904648564]\n"
     ]
    }
   ],
   "source": [
    "mu_lower = xbar + t_lower*s/np.sqrt(10)\n",
    "mu_upper = xbar + t_upper*s/np.sqrt(10)\n",
    "print([mu_lower, mu_upper])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualise the confidence interval\n",
    "xrange = np.arange(140, 220, .1)\n",
    "plt.hist(height_data, density=True)\n",
    "plt.axvline(xbar, linestyle='-', color=\"blue\", ymin=0, ymax=1)\n",
    "plt.plot([xbar-s/np.sqrt(10), xbar+s/np.sqrt(10)], [0.1,0.1], linestyle='-', color=\"blue\")\n",
    "plt.axvline(mu_lower, linestyle='--', color=\"blue\", ymin=0, ymax=1)\n",
    "plt.axvline(mu_upper, linestyle='--', color=\"blue\", ymin=0, ymax=1)\n",
    "plt.ylim(0,.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also calcualte a 99%-confidence interval for our mean student height\n",
    "\n",
    "Will it be wider or narrower ?\n",
    "\n",
    "Try to calculate the 99% interval using Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulation: Distribution of the sample variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "151.4176930076104\n",
      "144\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Back to simulation of student heights\n",
    "mu = 178\n",
    "sigma = 12\n",
    "n = 10\n",
    "\n",
    "# calculate sample VARIANCE\n",
    "x = stats.norm.rvs(mu, sigma, size=n)\n",
    "print(x.var())\n",
    "print(sigma**2)\n",
    "\n",
    "# Plot histogram \n",
    "plt.hist(x, density=True)\n",
    "plt.xlim(150,220)\n",
    "plt.ylim(0,0.20)\n",
    "plt.axvline(x.mean(), linestyle='--', color=\"black\")\n",
    "plt.plot([x.mean()-x.std(),x.mean()+x.std()], [.1, .1], '|', linestyle=\"-\", color='grey')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not only sample mean changes for each simulation - also the sample variance changes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TJCkhIUFLly7VqlWrlJ2draysLK1cuVIZGRny+/2SpOuuuy6mD1deeaUk6YYbbtC1117b78EDAAD7xR12CgsLdfz4cVVUVCgUCik3N1f19fXRG4xbW1uVmPjFgtGsWbO0efNmlZeXa8WKFcrOzlZdXZ2mTp0arVm+fLkikYgWL16s9vZ2zZ49W/X19XI4HBdhiAAAYChLMMaYwe7EQAiHw3I6nero6OD+nf9TVVU12F0ALprKysrB7gKAS+Bi/P6+LL6NBQAA0F+EHQAAYDXCDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAaoQdAABgNcIOAACwGmEHAABYjbADAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALAaYQcAAFiNsAMAAKxG2AEAAFYj7AAAAKsRdgAAgNUIOwAAwGqEHQAAYDXCDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAaoQdAABgNcIOAACwGmEHAABYjbADAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALAaYQcAAFiNsAMAAKxG2AEAAFYj7AAAAKv1K+xs3LhREydOlMPhkNvt1u7du/us37ZtmyZNmiSHw6Fp06Zpx44dMceNMaqoqFB6erpGjBghr9ergwcPxtT85V/+pa677jo5HA6lp6frvvvu05EjR/rTfQAAMITEHXa2bt2q0tJSVVZWau/evcrJyZHP59OxY8d6rd+1a5cWLFigkpISNTc3y+/3y+/3a//+/dGa1atXa/369aqtrVUwGNSoUaPk8/l0+vTpaM3tt9+un/3sZzpw4IB+/vOf6/3339df/dVf9WPIAABgKEkwxph4Grjdbt1yyy3asGGDJKm7u1uZmZl6+OGH9fjjj59TX1hYqEgkou3bt0f33XrrrcrNzVVtba2MMcrIyNCjjz6qxx57TJLU0dGhtLQ0vfjii5o/f36v/fi3f/s3+f1+dXZ26oorrvjKfofDYTmdTnV0dCglJSWeIVurqqpqsLsAXDSVlZWD3QUAl8DF+P0d18pOV1eXmpqa5PV6vzhBYqK8Xq8CgUCvbQKBQEy9JPl8vmh9S0uLQqFQTI3T6ZTb7T7vOU+ePKmXX35Zs2bNOm/Q6ezsVDgcjtkAAMDQE1fYOXHihM6ePau0tLSY/WlpaQqFQr22CYVCfdb3vF7IOX/wgx9o1KhRuvrqq9Xa2qpXX331vH2trq6W0+mMbpmZmRc2SAAAYJXL6ttYy5YtU3Nzs15//XUNGzZMCxcu1Pk+hSsrK1NHR0d0O3z48AD3FgAAfB0Mj6c4NTVVw4YNU1tbW8z+trY2uVyuXtu4XK4+63te29ralJ6eHlOTm5t7zs9PTU3VN77xDU2ePFmZmZn69a9/LY/Hc87PTU5OVnJycjzDAwAAFoprZScpKUl5eXlqbGyM7uvu7lZjY2OvgUOSPB5PTL0kNTQ0ROuzsrLkcrliasLhsILB4HnP2fNzpc/vzQEAADifuFZ2JKm0tFRFRUXKz8/XzJkzVVNTo0gkouLiYknSwoULNX78eFVXV0uSlixZojlz5mjt2rWaO3eutmzZoj179mjTpk2SpISEBC1dulSrVq1Sdna2srKytHLlSmVkZMjv90uSgsGgfvOb32j27NkaM2aM3n//fa1cuVI33HBDn4EIAAAg7rBTWFio48ePq6KiQqFQSLm5uaqvr4/eYNza2qrExC8WjGbNmqXNmzervLxcK1asUHZ2turq6jR16tRozfLlyxWJRLR48WK1t7dr9uzZqq+vl8PhkCSNHDlSv/jFL1RZWalIJKL09HQVFBSovLycj6oAAECf4n7OzuWK5+yci+fswCY8Zwew04A/ZwcAAOByw8rORcIqCYB4sRoFfDVWdgAAAL4CYQcAAFiNsAMAAKxG2AEAAFYj7AAAAKsRdgAAgNUIOwAAwGqEHQAAYDXCDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAaoQdAABgNcIOAACwGmEHAABYjbADAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALAaYQcAAFiNsAMAAKxG2AEAAFYj7AAAAKsRdgAAgNUIOwAAwGqEHQAAYDXCDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAaoQdAABgNcIOAACwGmEHAABYjbADAACsRtgBAABWI+wAAACr9SvsbNy4URMnTpTD4ZDb7dbu3bv7rN+2bZsmTZokh8OhadOmaceOHTHHjTGqqKhQenq6RowYIa/Xq4MHD0aPf/DBByopKVFWVpZGjBihG264QZWVlerq6upP9wEAwBASd9jZunWrSktLVVlZqb179yonJ0c+n0/Hjh3rtX7Xrl1asGCBSkpK1NzcLL/fL7/fr/3790drVq9erfXr16u2tlbBYFCjRo2Sz+fT6dOnJUnvvfeeuru79U//9E9699139Y//+I+qra3VihUr+jlsAAAwVCQYY0w8Ddxut2655RZt2LBBktTd3a3MzEw9/PDDevzxx8+pLywsVCQS0fbt26P7br31VuXm5qq2tlbGGGVkZOjRRx/VY489Jknq6OhQWlqaXnzxRc2fP7/XfqxZs0bPPfec/vCHP1xQv8PhsJxOpzo6OpSSkhLPkC9IVVXVRT8nALtVVlYOdheAr72L8fs7rpWdrq4uNTU1yev1fnGCxER5vV4FAoFe2wQCgZh6SfL5fNH6lpYWhUKhmBqn0ym3233ec0qfB6KxY8ee93hnZ6fC4XDMBgAAhp64ws6JEyd09uxZpaWlxexPS0tTKBTqtU0oFOqzvuc1nnMeOnRIzz77rL7//e+ft6/V1dVyOp3RLTMzs+/BAQAAK11238b68MMPVVBQoHvuuUeLFi06b11ZWZk6Ojqi2+HDhwewlwAA4OsirrCTmpqqYcOGqa2tLWZ/W1ubXC5Xr21cLlef9T2vF3LOI0eO6Pbbb9esWbO0adOmPvuanJyslJSUmA0AAAw9cYWdpKQk5eXlqbGxMbqvu7tbjY2N8ng8vbbxeDwx9ZLU0NAQrc/KypLL5YqpCYfDCgaDMef88MMPddtttykvL08vvPCCEhMvu0UpAAAwCIbH26C0tFRFRUXKz8/XzJkzVVNTo0gkouLiYknSwoULNX78eFVXV0uSlixZojlz5mjt2rWaO3eutmzZoj179kRXZhISErR06VKtWrVK2dnZysrK0sqVK5WRkSG/3y/pi6AzYcIE/ehHP9Lx48ej/TnfihIAAIDUj7BTWFio48ePq6KiQqFQSLm5uaqvr4/eYNza2hqz6jJr1ixt3rxZ5eXlWrFihbKzs1VXV6epU6dGa5YvX65IJKLFixervb1ds2fPVn19vRwOh6TPV4IOHTqkQ4cO6dprr43pT5zfnAcAAENM3M/ZuVzxnB0AXzc8Zwf4agP+nB0AAIDLDWEHAABYjbADAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALAaYQcAAFiNsAMAAKxG2AEAAFYj7AAAAKsRdgAAgNUIOwAAwGqEHQAAYDXCDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAaoQdAABgNcIOAACwGmEHAABYjbADAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALAaYQcAAFiNsAMAAKw2fLA7AAC4fFRVVQ12F+JWWVk52F3AIGNlBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAaoQdAABgNcIOAACwGmEHAABYjbADAACsRtgBAABW61fY2bhxoyZOnCiHwyG3263du3f3Wb9t2zZNmjRJDodD06ZN044dO2KOG2NUUVGh9PR0jRgxQl6vVwcPHoyp+eEPf6hZs2Zp5MiRGj16dH+6DQAAhqC4w87WrVtVWlqqyspK7d27Vzk5OfL5fDp27Fiv9bt27dKCBQtUUlKi5uZm+f1++f1+7d+/P1qzevVqrV+/XrW1tQoGgxo1apR8Pp9Onz4drenq6tI999yjBx54oB/DBAAAQ1XcYWfdunVatGiRiouLNWXKFNXW1mrkyJF6/vnne61/5plnVFBQoGXLlmny5Ml66qmnNGPGDG3YsEHS56s6NTU1Ki8v17x58zR9+nS99NJLOnLkiOrq6qLnqaqq0iOPPKJp06b1b6QAAGBIiivsdHV1qampSV6v94sTJCbK6/UqEAj02iYQCMTUS5LP54vWt7S0KBQKxdQ4nU653e7znvNCdHZ2KhwOx2wAAGDoiSvsnDhxQmfPnlVaWlrM/rS0NIVCoV7bhEKhPut7XuM554Worq6W0+mMbpmZmf0+FwAAuHxZ+22ssrIydXR0RLfDhw8PdpcAAMAgiCvspKamatiwYWpra4vZ39bWJpfL1Wsbl8vVZ33PazznvBDJyclKSUmJ2QAAwNAzPJ7ipKQk5eXlqbGxUX6/X5LU3d2txsZGPfTQQ7228Xg8amxs1NKlS6P7Ghoa5PF4JElZWVlyuVxqbGxUbm6uJCkcDisYDPLNKwBWq6qqGuwuAENCXGFHkkpLS1VUVKT8/HzNnDlTNTU1ikQiKi4uliQtXLhQ48ePV3V1tSRpyZIlmjNnjtauXau5c+dqy5Yt2rNnjzZt2iRJSkhI0NKlS7Vq1SplZ2crKytLK1euVEZGRjRQSVJra6tOnjyp1tZWnT17Vvv27ZMk3Xjjjbryyiv/yGkAAAC2ijvsFBYW6vjx46qoqFAoFFJubq7q6+ujNxi3trYqMfGLT8dmzZqlzZs3q7y8XCtWrFB2drbq6uo0derUaM3y5csViUS0ePFitbe3a/bs2aqvr5fD4YjWVFRU6Cc/+Un03zfffLMk6Y033tBtt90W98ABAMDQkGCMMYPdiYEQDofldDrV0dFxSe7fYTkaAL6eKisrB7sL+CNcjN/f1n4bCwAAQCLsAAAAyxF2AACA1Qg7AADAaoQdAABgNcIOAACwGmEHAABYjbADAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALDa8MHuAAAAOFdVVdVgdyFulZWVg92FXrGyAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAaoQdAABgNcIOAACwGmEHAABYjbADAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALAaYQcAAFiNsAMAAKxG2AEAAFYj7AAAAKsRdgAAgNUIOwAAwGqEHQAAYDXCDgAAsBphBwAAWI2wAwAArEbYAQAAViPsAAAAqxF2AACA1Qg7AADAaoQdAABgNcIOAACwGmEHAABYrV9hZ+PGjZo4caIcDofcbrd2797dZ/22bds0adIkORwOTZs2TTt27Ig5boxRRUWF0tPTNWLECHm9Xh08eDCm5uTJk7r33nuVkpKi0aNHq6SkRB9//HF/ug8AAIaQuMPO1q1bVVpaqsrKSu3du1c5OTny+Xw6duxYr/W7du3SggULVFJSoubmZvn9fvn9fu3fvz9as3r1aq1fv161tbUKBoMaNWqUfD6fTp8+Ha2599579e6776qhoUHbt2/X22+/rcWLF/djyAAAYCiJO+ysW7dOixYtUnFxsaZMmaLa2lqNHDlSzz//fK/1zzzzjAoKCrRs2TJNnjxZTz31lGbMmKENGzZI+nxVp6amRuXl5Zo3b56mT5+ul156SUeOHFFdXZ0k6fe//73q6+v14x//WG63W7Nnz9azzz6rLVu26MiRI/0fPQAAsN7weIq7urrU1NSksrKy6L7ExER5vV4FAoFe2wQCAZWWlsbs8/l80SDT0tKiUCgkr9cbPe50OuV2uxUIBDR//nwFAgGNHj1a+fn50Rqv16vExEQFg0F9+9vfPufndnZ2qrOzM/rvjo4OSVI4HI5nyBfs/69CAQC+Pi7V/+5fapfj75VLMdc95zTG9PsccYWdEydO6OzZs0pLS4vZn5aWpvfee6/XNqFQqNf6UCgUPd6zr6+acePGxXZ8+HCNHTs2WvNl1dXVqqqqOmd/Zmbm+YYHALDQ008/PdhdGDIu5VyfOnVKTqezX23jCjuXk7KyspgVpe7ubp08eVJXX321EhISBrFnl1Y4HFZmZqYOHz6slJSUwe7O1w7z0zfmp2/MT9+Yn74xP+fX19wYY3Tq1CllZGT0+/xxhZ3U1FQNGzZMbW1tMfvb2trkcrl6beNyufqs73lta2tTenp6TE1ubm605ss3QJ85c0YnT548789NTk5WcnJyzL7Ro0f3PUCLpKSk8GbqA/PTN+anb8xP35ifvjE/53e+uenvik6PuG5QTkpKUl5enhobG6P7uru71djYKI/H02sbj8cTUy9JDQ0N0fqsrCy5XK6YmnA4rGAwGK3xeDxqb29XU1NTtGbnzp3q7u6W2+2OZwgAAGCIiftjrNLSUhUVFSk/P18zZ85UTU2NIpGIiouLJUkLFy7U+PHjVV1dLUlasmSJ5syZo7Vr12ru3LnasmWL9uzZo02bNkmSEhIStHTpUq1atUrZ2dnKysrSypUrlZGRIb/fL0maPHmyCgoKtGjRItXW1uqzzz7TQw89pPnz5/9Ry1oAAMB+cYedwsJCHT9+XBUVFQqFQsrNzVV9fX30BuPW1lYlJn6xYDRr1ixt3rxZ5eXlWrFihbKzs1VXV6epU6dGa5YvX65IJKLFixervb1ds2fPVn19vRwOR7Tm5Zdf1kMPPaQ77rhDiYmJuvvuu7V+/fo/ZuxWSk5OVmVl5Tkf4eFzzE/fmJ++MT99Y376xvyc36WemwTzx3yXCwAA4GuOv40FAACsRtgBAABWI+wAAACrEXYAAIDVCDuXoSeeeEIJCQkx26RJk6LHT58+rQcffFBXX321rrzySt19993nPNjRJm+//bb+4i/+QhkZGUpISIj+3bUexhhVVFQoPT1dI0aMkNfr1cGDB2NqTp48qXvvvVcpKSkaPXq0SkpK9PHHHw/gKC6dr5qf733ve+dcTwUFBTE1Ns9PdXW1brnlFl111VUaN26c/H6/Dhw4EFNzIe+p1tZWzZ07VyNHjtS4ceO0bNkynTlzZiCHctFdyNzcdttt51w/999/f0yNjXMjSc8995ymT58efRCex+PRa6+9Fj0+VK+bHl81PwN57RB2LlN/8id/oqNHj0a3X/7yl9FjjzzyiP793/9d27Zt01tvvaUjR47oO9/5ziD29tKKRCLKycnRxo0bez2+evVqrV+/XrW1tQoGgxo1apR8Pl/MH9m799579e6776qhoUHbt2/X22+/rcWLFw/UEC6pr5ofSSooKIi5nn7605/GHLd5ft566y09+OCD+vWvf62GhgZ99tlnuvPOOxWJRKI1X/WeOnv2rObOnauuri7t2rVLP/nJT/Tiiy+qoqJiMIZ00VzI3EjSokWLYq6f1atXR4/ZOjeSdO211+rpp59WU1OT9uzZoz/7sz/TvHnz9O6770oautdNj6+aH2kArx2Dy05lZaXJycnp9Vh7e7u54oorzLZt26L7fv/73xtJJhAIDFAPB48k88orr0T/3d3dbVwul1mzZk10X3t7u0lOTjY//elPjTHG/Nd//ZeRZH7zm99Ea1577TWTkJBgPvzwwwHr+0D48vwYY0xRUZGZN2/eedsMpfkxxphjx44ZSeatt94yxlzYe2rHjh0mMTHRhEKhaM1zzz1nUlJSTGdn58AO4BL68twYY8ycOXPMkiVLzttmqMxNjzFjxpgf//jHXDfn0TM/xgzstcPKzmXq4MGDysjI0PXXX697771Xra2tkqSmpiZ99tln8nq90dpJkybpuuuuUyAQGKzuDpqWlhaFQqGY+XA6nXK73dH5CAQCGj16tPLz86M1Xq9XiYmJCgaDA97nwfDmm29q3Lhxuummm/TAAw/oo48+ih4bavPT0dEhSRo7dqykC3tPBQIBTZs2LfpwVUny+XwKh8Mx/y/2cvfluenx8ssvKzU1VVOnTlVZWZk++eST6LGhMjdnz57Vli1bFIlE5PF4uG6+5Mvz02Ogrh1r/+q5zdxut1588UXddNNNOnr0qKqqqvSnf/qn2r9/v0KhkJKSks75o6dpaWkKhUKD0+FB1DPm//9m6fl3z7FQKKRx48bFHB8+fLjGjh07JOasoKBA3/nOd5SVlaX3339fK1as0F133aVAIKBhw4YNqfnp7u7W0qVL9c1vfjP6lPcLeU+FQqFer7GeYzbobW4k6bvf/a4mTJigjIwMvfPOO/rBD36gAwcO6Be/+IUk++fmd7/7nTwej06fPq0rr7xSr7zyiqZMmaJ9+/Zx3ej88yMN7LVD2LkM3XXXXdH/nj59utxutyZMmKCf/exnGjFixCD2DJej+fPnR/972rRpmj59um644Qa9+eabuuOOOwaxZwPvwQcf1P79+2PugcPnzjc3///erWnTpik9PV133HGH3n//fd1www0D3c0Bd9NNN2nfvn3q6OjQv/7rv6qoqEhvvfXWYHfra+N88zNlypQBvXb4GMsCo0eP1je+8Q0dOnRILpdLXV1dam9vj6lpa2uTy+UanA4Oop4xf/kbEP9/Plwul44dOxZz/MyZMzp58uSQnLPrr79eqampOnTokKShMz8PPfSQtm/frjfeeEPXXnttdP+FvKdcLlev11jPscvd+eamN263W5Jirh+b5yYpKUk33nij8vLyVF1drZycHD3zzDNcN//nfPPTm0t57RB2LPDxxx/r/fffV3p6uvLy8nTFFVeosbExevzAgQNqbW2N+Zx0qMjKypLL5YqZj3A4rGAwGJ0Pj8ej9vZ2NTU1RWt27typ7u7u6JtvKPmf//kfffTRR0pPT5dk//wYY/TQQw/plVde0c6dO5WVlRVz/ELeUx6PR7/73e9iQmFDQ4NSUlKiS/aXo6+am97s27dPkmKuHxvn5ny6u7vV2dk5pK+bvvTMT28u6bXTj5upMcgeffRR8+abb5qWlhbzq1/9yni9XpOammqOHTtmjDHm/vvvN9ddd53ZuXOn2bNnj/F4PMbj8Qxyry+dU6dOmebmZtPc3GwkmXXr1pnm5mbz3//938YYY55++mkzevRo8+qrr5p33nnHzJs3z2RlZZlPP/00eo6CggJz8803m2AwaH75y1+a7Oxss2DBgsEa0kXV1/ycOnXKPPbYYyYQCJiWlhbzn//5n2bGjBkmOzvbnD59OnoOm+fngQceME6n07z55pvm6NGj0e2TTz6J1nzVe+rMmTNm6tSp5s477zT79u0z9fX15pprrjFlZWWDMaSL5qvm5tChQ+bJJ580e/bsMS0tLebVV181119/vfnWt74VPYetc2OMMY8//rh56623TEtLi3nnnXfM448/bhISEszrr79ujBm6102PvuZnoK8dws5lqLCw0KSnp5ukpCQzfvx4U1hYaA4dOhQ9/umnn5q//du/NWPGjDEjR4403/72t83Ro0cHsceX1htvvGEknbMVFRUZYz7/+vnKlStNWlqaSU5ONnfccYc5cOBAzDk++ugjs2DBAnPllVealJQUU1xcbE6dOjUIo7n4+pqfTz75xNx5553mmmuuMVdccYWZMGGCWbRoUcxXPY2xe356mxtJ5oUXXojWXMh76oMPPjB33XWXGTFihElNTTWPPvqo+eyzzwZ4NBfXV81Na2ur+da3vmXGjh1rkpOTzY033miWLVtmOjo6Ys5j49wYY8zf/M3fmAkTJpikpCRzzTXXmDvuuCMadIwZutdNj77mZ6CvnQRjjIlvLQgAAODywT07AADAaoQdAABgNcIOAACwGmEHAABYjbADAACsRtgBAABWI+wAAACrEXYAAIDVCDsAAMBqhB0AAGA1wg4AALAaYQcAAFjtfwEqLYIlyoIHvQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Repeat 100 times and plot histogram of the variance values\n",
    "\n",
    "# Draw (10 x 100) random numbers\n",
    "mat = stats.norm.rvs(mu, sigma, size=(n,100))\n",
    "\n",
    "# Calculate sample mean of each column \n",
    "s2 = mat.var(axis=0)\n",
    "\n",
    "plt.hist(s2, density=True, color=\"grey\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variance is always positive and does not follow a normal distribution. <br>\n",
    "The distribution of variance is not symmestric. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Variance of student heights "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "149.11111111111111\n"
     ]
    }
   ],
   "source": [
    "# A random sample of n = 10 student height have the following sample mean and variance:\n",
    "height_data = np.array([168, 161, 167, 179, 184, 166, 198, 187, 191, 179])\n",
    "xbar = height_data.mean()\n",
    "s = height_data.std(ddof=1)\n",
    "n=10\n",
    "\n",
    "var_hat = s**2\n",
    "print(var_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot chi-square distribution with n-1 = 9 degrees of freedom\n",
    "plt.plot(np.arange(0,50,.1), stats.chi2.pdf(np.arange(0,50,.1), df=(n-1), loc=0, scale=1), color=\"red\")\n",
    "xint = np.arange(0, stats.chi2.ppf(0.025, df=(n-1), loc=0, scale=1), .01)\n",
    "plt.fill_between(xint, stats.chi2.pdf(xint, df=(n-1), loc=0, scale=1), color='red', alpha=0.3)\n",
    "xint = np.arange(stats.chi2.ppf(0.975, df=(n-1), loc=0, scale=1), 50, .01)\n",
    "plt.fill_between(xint, stats.chi2.pdf(xint, df=(n-1), loc=0, scale=1), color='red', alpha=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.7003894999803584, 19.02276779864163]\n"
     ]
    }
   ],
   "source": [
    "chi2_lower = stats.chi2.ppf(0.025, df=(n-1), loc=0, scale=1)\n",
    "chi2_upper = stats.chi2.ppf(0.975, df=(n-1), loc=0, scale=1)\n",
    "\n",
    "print([chi2_lower, chi2_upper])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "149.11111111111111\n",
      "496.96534518807795\n",
      "70.5470420606106\n"
     ]
    }
   ],
   "source": [
    "# confidence interval for the variance\n",
    "print(var_hat)\n",
    "print((n-1)*var_hat/chi2_lower)\n",
    "print((n-1)*var_hat/chi2_upper)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.211106056009468\n",
      "22.29271955567732\n",
      "8.399228658669236\n"
     ]
    }
   ],
   "source": [
    "# confidence interval for the standard deviation\n",
    "print(np.sqrt(var_hat))\n",
    "print(np.sqrt((n-1)*var_hat/chi2_lower))\n",
    "print(np.sqrt((n-1)*var_hat/chi2_upper))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice the interval is not symmetric"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CLT in action"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=1\n",
    "k=1000\n",
    "u = stats.uniform.rvs(loc=0, scale=30, size=(n,k))\n",
    "\n",
    "mean_values = u.mean(axis=0)\n",
    "\n",
    "plt.hist(mean_values, density=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now increase n to 2,3,6,30"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also try with another distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=1\n",
    "k=1000\n",
    "u = stats.expon.rvs(loc=0, scale=30, size=(n,k))\n",
    "mean_values = u.mean(axis=0)\n",
    "\n",
    "plt.hist(mean_values, density=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now increase n to 2,3,6,30"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Exam question from 2016 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grades = [2,4,7,10,12]\n",
    "count = [22,78,84,72,24]\n",
    "plt.bar(grades,count)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.9714285714285715\n"
     ]
    }
   ],
   "source": [
    "# calculate average (mean) grade:\n",
    "avg_grade = np.sum(np.array(grades)*np.array(count)/280)\n",
    "print(avg_grade)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.97142857, -2.97142857,  0.02857143,  3.02857143,  5.02857143])"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grades-avg_grade"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.959754224270354\n"
     ]
    }
   ],
   "source": [
    "# calculate variance of grades:\n",
    "var_grade = 1/(280-1)*np.sum(np.array(count) * (grades-avg_grade)**2)\n",
    "print(var_grade)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.17888298474012831\n"
     ]
    }
   ],
   "source": [
    "avg_grade_standard_error = np.sqrt(var_grade)/np.sqrt(280)\n",
    "print(avg_grade_standard_error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.968503126548004\n"
     ]
    }
   ],
   "source": [
    "t_upper = stats.t.ppf(0.975, df=280-1)\n",
    "print(t_upper)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.61929685668139\n",
      "7.323560286175753\n"
     ]
    }
   ],
   "source": [
    "print(avg_grade - t_upper*avg_grade_standard_error)\n",
    "print(avg_grade + t_upper*avg_grade_standard_error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Production of tablets "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.004900000000000001\n"
     ]
    }
   ],
   "source": [
    "# A random sample of n = 20 have the following sample mean and variance:\n",
    "\n",
    "n = 20\n",
    "mu_hat = 1.01\n",
    "var_hat = 0.07**2\n",
    "\n",
    "print(var_hat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to give a confidence interval on the estimate of var_hat\n",
    "\n",
    "We choose a 95% confidence interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot chi-square distribution and visualise the limits of chi^2\n",
    "\n",
    "# we need the distribution of n-1 = 19 degrees of freedom\n",
    "\n",
    "plt.plot(np.arange(0,50,.1), stats.chi2.pdf(np.arange(0,50,.1), df=(n-1), loc=0, scale=1), color=\"red\")\n",
    "xint = np.arange(0, stats.chi2.ppf(0.025, df=(n-1), loc=0, scale=1), .01)\n",
    "plt.fill_between(xint, stats.chi2.pdf(xint, df=(n-1), loc=0, scale=1), color='peachpuff', alpha=0.6)\n",
    "xint = np.arange(stats.chi2.ppf(0.975, df=(n-1), loc=0, scale=1), 50, .01)\n",
    "plt.fill_between(xint, stats.chi2.pdf(xint, df=(n-1), loc=0, scale=1), color='peachpuff', alpha=0.6)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[8.906516481987971, 32.85232686172969]\n"
     ]
    }
   ],
   "source": [
    "chi2_lower = stats.chi2.ppf(0.025, df=(n-1), loc=0, scale=1)\n",
    "chi2_upper = stats.chi2.ppf(0.975, df=(n-1), loc=0, scale=1)\n",
    "\n",
    "print([chi2_lower,chi2_upper])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.004900000000000001\n",
      "0.010453020570756269\n",
      "0.002833893635353239\n"
     ]
    }
   ],
   "source": [
    "# confidence interval for the variance\n",
    "print(var_hat)\n",
    "print((n-1)*var_hat/chi2_lower)\n",
    "print((n-1)*var_hat/chi2_upper)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.07\n",
      "0.10224001452834536\n",
      "0.053234327603091214\n"
     ]
    }
   ],
   "source": [
    "# confidence interval for the standard deviation\n",
    "print(np.sqrt(var_hat))\n",
    "print(np.sqrt((n-1)*var_hat/chi2_lower))\n",
    "print(np.sqrt((n-1)*var_hat/chi2_upper))"
   ]
  }
 ],
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