.ipynb_checkpoints/homework-checkpoint (Case Conflict 49).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Homework code\n",
    "\n",
    "\n",
    "\n",
    " #### [Back to main page](https://petrosyan.page/fall2020math3215)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "# library\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "plt.rcParams[\"figure.figsize\"] = (8, 5)\n",
    "plt.gca().spines['top'].set_visible(False)\n",
    "plt.gca().spines['right'].set_visible(False)\n",
    "plt.gca().spines['bottom'].set_visible(False)\n",
    "\n",
    "data=np.array([1,6,9,9,3,8,5,0,6,7,5,7,5,9,4,6,5,6,4,4,4,8,0,9,3,2,1,5,4,5,7,3,2,\n",
    "      1,4,6,7,1,3,4,4,8,8,6,1,6,1,2,8,8,1,7,8,2,2,0,9,7,5,2,5,7,1,7,0,1,\n",
    "      8,5,2,9,2,4,7,6,6,6,3,3,6,9,6,0,2,3,6,0,1,7,8,9,1,3,7,0,9,8,5,3,4,\n",
    "      8,2,6,6,4,2,7,5,0,8,2,7,6,8,9,9,7,9,0,0,0,9,3,3,4,5,1,9,4,5,4,6,4,\n",
    "      8,7,6,8,6,6,2,3,6,6,1,7,4,1,8,9,8,8])\n",
    "\n",
    "range_x=np.arange(0,10)\n",
    "pmf_values=np.ones(range_x.size)/range_x.size \n",
    "\n",
    "# compute empirical pmf\n",
    "def epmf(data):\n",
    "    erange_x, counts = np.unique(data, return_counts=True)\n",
    "    epmf_values = counts/data.size\n",
    "    return epmf_values, erange_x\n",
    "\n",
    "epmf_values, erange_x = epmf(data)\n",
    "\n",
    "# plot \n",
    "plt.ylim(0,0.2) \n",
    "plt.axhline(y=0, color='k')\n",
    "plt.xticks(range_x)\n",
    "\n",
    "plt.scatter(range_x,np.zeros(range_x.shape), color =\"red\", s=20)\n",
    "plt.bar(range_x, pmf_values, width=1, color='#039be5', edgecolor=\"w\", linewidth=1.3,  label=\"True histogran\")\n",
    "plt.bar(erange_x, epmf_values, width=0.9, color=(1, 1, 1, 0), \n",
    "        edgecolor='green', linewidth=1.5,linestyle=\"--\", label=\"Relative frequency histogram\")\n",
    "plt.legend()\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "range_x=np.arange(0,10)\n",
    "pmf_values=np.ones(range_x.size)/range_x.size\n",
    "\n",
    "fig, ax2 = plt.subplots(num=1, clear=True)\n",
    "\n",
    "\n",
    "ax2.set_ylim(-0.01, 0.2) \n",
    "ax2.set_xlim(-0.7, 10)\n",
    "ax2.axhline(y=0, color='k')\n",
    "ax2.set_xticks(range_x)\n",
    "ax2.set_yticks(pmf_values)\n",
    "ax2.spines[\"top\"].set_visible(False)  \n",
    "ax2.spines[\"right\"].set_visible(False)\n",
    "ax2.spines[\"bottom\"].set_visible(False)\n",
    "\n",
    "\n",
    "# PLotting with plt.bar instead of plt.hist works better when f(x) are knowwn\n",
    "ax2.scatter(range_x,np.zeros(range_x.shape), color =\"red\", s=20)\n",
    "ax2.bar(range_x, pmf_values, width=1, color='#039be5', edgecolor=\"w\", linewidth=1.3, label=\"Histogran\")\n",
    "ax2.set_title(\"Histogram\")\n",
    "\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1312,& 0.0747,& 0.2818,& 0.7537,& 0.9015,& 0.7973,& 0.6686,& 0.0377,&0.3207,& 0.0497,& 0.3036,& 0.7613,& 0.1278,& 0.3596,& 0.4977,& 0.0802,&0.5065,& 0.6308,& 0.1961,& 0.921 ,& 0.2606,& 0.6621,& 0.5593,& 0.1525,&0.0694,& 0.6032,& 0.2863,& 0.2178,& 0.7832,& 0.5217,& 0.7545,& 0.3325,&0.5476,& 0.7367,& 0.0873,& 0.8538,& 0.3113,& 0.5907,& 0.7813,& 0.0143\n"
     ]
    }
   ],
   "source": [
    "import re\n",
    "\n",
    "text=\"169 938 506 757 594 656 444 809 321 545 732 146 713 448 861 612 881 782 209 752 571 701 852 924 766 633 696 023 601 789 137 098 534 826 642 750 827 689 979 000 933 451 945 464 876 866 236 617 418 988\"\n",
    "\n",
    "newtext=re.sub(r\"\\s\",\"\",text)\n",
    "\n",
    "re.sub(r\"(\\d)\",r\"\\g<1>,\",newtext)\n",
    "\n",
    "text = \"0.1312, 0.0747, 0.2818, 0.7537, 0.9015, 0.7973, 0.6686, 0.0377,0.3207, 0.0497, 0.3036, 0.7613, 0.1278, 0.3596, 0.4977, 0.0802,0.5065, 0.6308, 0.1961, 0.921 , 0.2606, 0.6621, 0.5593, 0.1525,0.0694, 0.6032, 0.2863, 0.2178, 0.7832, 0.5217, 0.7545, 0.3325,0.5476, 0.7367, 0.0873, 0.8538, 0.3113, 0.5907, 0.7813, 0.0143\"\n",
    "\n",
    "newtext=re.sub(r\",\",\",&\",text)\n",
    "print(newtext)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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J/jbJA5ZdtKkvJ/nyujMt52Ut6DvVo5N8pLu/tvSQTTwqyUXdfXl3X5vkHUkevPCmXU3AucmtvjjsdUk+092vWHrPVqrqdlV1+urtE7P2P6TPLrvqxrr7Rd19l+4+M2unUv+lu3fcUU5Vnbz6gsWsTkn/fJId950S3f3VJF+qqrNW73pkkh31xZUbPDk78PT5yheTPLCqTlr9nn9k1r7ehZuIgA9XVW9OckGSs6rqy1X1jKU3beIhSX4la0eLB78N5jFLj9rEHZO8v6o+nuTDWXsNfMd+m9YOd4ck51fVx5J8KMk/dPd7F960lWcnedPq1/2+SV668J5NVdVJSX4ua0e2O87qLMZ5ST6S5BNZ64u/ke0m5NvIAGAgR+AAMJCAA8BAAg4AAwk4AAwk4AAwkIADwEACDgADCTgADPT/s1Z5HO7akIQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "range_x=np.arange(1,9)\n",
    "pmf_values=np.ones(range_x.size)/range_x.size\n",
    "\n",
    "fig, ax2 = plt.subplots(num=1, clear=True)\n",
    "\n",
    "\n",
    "ax2.set_ylim(-0.01, 0.2) \n",
    "ax2.set_xlim(-0.7, 10)\n",
    "ax2.axhline(y=0, color='k')\n",
    "ax2.set_xticks(range_x)\n",
    "ax2.set_yticks(pmf_values)\n",
    "ax2.spines[\"top\"].set_visible(False)  \n",
    "ax2.spines[\"right\"].set_visible(False)\n",
    "ax2.spines[\"bottom\"].set_visible(False)\n",
    "\n",
    "\n",
    "# PLotting with plt.bar instead of plt.hist works better when f(x) are knowwn\n",
    "ax2.scatter(range_x,np.zeros(range_x.shape), color =\"red\", s=20)\n",
    "ax2.bar(range_x, pmf_values, width=1, color='#039be5', edgecolor=\"w\", linewidth=1.3, label=\"Histogran\")\n",
    "ax2.set_title(\"Histogram\")\n",
    "\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "range_x=np.array([-1,1,2,3,4])\n",
    "pmf_values=np.array([1/4,1/12,1/6,2/6,1/6])\n",
    "\n",
    "fig, ax2 = plt.subplots(num=1, clear=True)\n",
    "\n",
    "\n",
    "ax2.set_ylim(-0.01, 0.4) \n",
    "ax2.set_xlim(-2, 5)\n",
    "ax2.axhline(y=0, color='k')\n",
    "ax2.set_xticks(range_x)\n",
    "ax2.set_yticks(pmf_values)\n",
    "ax2.spines[\"top\"].set_visible(False)  \n",
    "ax2.spines[\"right\"].set_visible(False)\n",
    "ax2.spines[\"bottom\"].set_visible(False)\n",
    "\n",
    "\n",
    "# PLotting with plt.bar instead of plt.hist works better when f(x) are knowwn\n",
    "ax2.scatter(range_x,np.zeros(range_x.shape), color =\"red\", s=20, zorder=2)\n",
    "ax2.bar(range_x, pmf_values, width=1, color='#039be5', edgecolor=\"w\", linewidth=1.3, label=\"Histogran\", zorder=1)\n",
    "ax2.set_title(\"Histogram\")\n",
    "\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from ipywidgets import interact, FloatSlider\n",
    "plt.rcParams['figure.figsize'] = (12, 8)\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "lmbd = 0.8\n",
    "x=1\n",
    "\n",
    "def cdf_func(xdata):\n",
    "    val = np.piecewise(xdata, \n",
    "                       [xdata<0, xdata==0, (xdata>0) & (xdata<1),  \n",
    "                        xdata==1, (xdata>1) & (xdata<2), xdata==2,\n",
    "                        (xdata>2) & (xdata<3), xdata==3,\n",
    "                       xdata>3], \n",
    "                       [0, np.nan, 1/2, np.nan, 0, np.nan, 1/2, np.nan, 0])\n",
    "    return val\n",
    "xdata = np.linspace(-0.5, 3.5, 1000)\n",
    "plt.plot(xdata,  cdf_func(xdata), linewidth=3)\n",
    "xshade = xdata[xdata<=x]\n",
    "plt.ylim(0, 0.6)\n",
    "plt.gca().spines['top'].set_visible(False)\n",
    "plt.gca().spines['right'].set_visible(False)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from ipywidgets import interact, FloatSlider\n",
    "plt.rcParams['figure.figsize'] = (12, 8)\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "lmbd = 0.8\n",
    "x=1\n",
    "\n",
    "def func(xdata):\n",
    "    f = lambda y: np.divide(y,2)\n",
    "    return f(xdata)\n",
    "\n",
    "def cdf_func(xdata):\n",
    "    val = np.piecewise(xdata, \n",
    "                       [xdata<=0, (xdata>0) & (xdata<1),  \n",
    "                         (xdata>=1) & (xdata<=2), \n",
    "                        (xdata>2) & (xdata<3),\n",
    "                       xdata>=3], \n",
    "                       [0, lambda x: x/2, 1/2,  lambda x: x/2-1/2,  1])\n",
    "    return val\n",
    "\n",
    "xdata = np.linspace(-0.5, 3.5, 1000)\n",
    "plt.plot(xdata,  cdf_func(xdata), linewidth=3)\n",
    "xshade = xdata[xdata<=x]\n",
    "plt.ylim(0, 1.1)\n",
    "plt.gca().spines['top'].set_visible(False)\n",
    "plt.gca().spines['right'].set_visible(False)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##midterm 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from ipywidgets import interact, FloatSlider\n",
    "plt.rcParams['figure.figsize'] = (12, 8)\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "lmbd = 0.8\n",
    "x=1\n",
    "\n",
    "def cdf_func(xdata):\n",
    "    val = np.piecewise(xdata, \n",
    "                       [xdata<0, xdata==0, (xdata>0) & (xdata<1),  \n",
    "                        xdata==1, (xdata>1) & (xdata<2), xdata==2,\n",
    "                        (xdata>2) & (xdata<3), xdata==3,\n",
    "                       xdata>3], \n",
    "                       [0, np.nan, 0.75, np.nan, 0, np.nan, 0.25, np.nan, 0])\n",
    "    return val\n",
    "xdata = np.linspace(-0.5, 3.5, 1000)\n",
    "plt.plot(xdata,  cdf_func(xdata), linewidth=3)\n",
    "xshade = xdata[xdata<=x]\n",
    "plt.ylim(-0.005, 0.8)\n",
    "plt.gca().spines['top'].set_visible(False)\n",
    "plt.gca().spines['right'].set_visible(False)\n",
    "plt.title(\"pdf of X\")\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from ipywidgets import interact, FloatSlider\n",
    "plt.rcParams['figure.figsize'] = (12, 8)\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "lmbd = 0.8\n",
    "x=1\n",
    "\n",
    "def func(xdata):\n",
    "    f = lambda y: np.divide(y,2)\n",
    "    return f(xdata)\n",
    "\n",
    "def cdf_func(xdata):\n",
    "    val = np.piecewise(xdata, \n",
    "                       [xdata<=0, (xdata>0) & (xdata<1),  \n",
    "                         (xdata>=1) & (xdata<=2), \n",
    "                        (xdata>2) & (xdata<3),\n",
    "                       xdata>=3], \n",
    "                       [0, lambda x: 0.75*x, 0.75,  lambda x: 0.75+0.25*(x-2),  1])\n",
    "    return val\n",
    "\n",
    "xdata = np.linspace(-1, 4, 1000)\n",
    "plt.plot(xdata,  cdf_func(xdata), linewidth=3)\n",
    "xshade = xdata[xdata<=x]\n",
    "plt.ylim(-0.005, 1.1)\n",
    "plt.gca().spines['top'].set_visible(False)\n",
    "plt.gca().spines['right'].set_visible(False)\n",
    "plt.title(\"cdf of X\")\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4\n",
      "[0.03278689 0.06557377 0.39344262 0.16393443]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams[\"figure.figsize\"] = (8, 4)\n",
    "\n",
    "\n",
    "\n",
    "data = np.array([ -1.42, -0.31, -0.73, -0.51, -2.23, -0.32, 1.38, 0.32, -0.66, 0.01,\n",
    "        -0.7, -1.86, -1.07, 0.1, -0.59, 0.58, -0.63, -0.87, -4.65, -1.14 ])\n",
    "\n",
    "def epmf(data, inter, N):\n",
    "    epmf_values = np.zeros(N)\n",
    "    for i in range(N): \n",
    "        length = inter[i+1]-inter[i]\n",
    "        epmf_values[i] = np.sum((inter[i]<=data) & (data<inter[i+1]))/(data.size*length)\n",
    "    return epmf_values \n",
    "    \n",
    "def dens_hist_std(data, N=4):\n",
    "    zmax = np.ceil(np.max(data)*10**1)/10**1\n",
    "    zmin = np.floor(np.min(data)*10**1)/10**1\n",
    "    print(zmax)\n",
    "    inter = np.linspace(zmin,zmax,N+1)   \n",
    "    length = inter[1]-inter[0]\n",
    "    epmf_values = epmf(data, inter, N)\n",
    "    print(epmf_values)\n",
    "    \n",
    "    plt.bar(inter[:N], epmf_values, width=length, \n",
    "            color='#039be5', edgecolor='black', linewidth=1, \n",
    "            align=\"edge\", label=\"True histogran\")\n",
    "    plt.figtext(0.8,0.8, \"N = {}\".format(N), ha=\"left\", va=\"top\",\n",
    "        backgroundcolor=(0.1, 0.1, 1, 0.15), fontsize=\"large\")\n",
    "    plt.xlim(zmin-0.5, zmax+0.5)\n",
    "    plt.ylim(0, np.max(epmf_values)+0.1)\n",
    "    plt.title(\"Density histogram of data\")\n",
    "    plt.gca().spines['top'].set_visible(False)\n",
    "    plt.gca().spines['right'].set_visible(False)\n",
    " \n",
    "dens_hist_std(data, 4)\n",
    "\n",
    "plt.show();\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.special import gamma \n",
    "from ipywidgets import interact, FloatSlider\n",
    "plt.rcParams['figure.figsize'] = (12, 8)\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams.update(mpl.rcParamsDefault)\n",
    "\n",
    "mu=0\n",
    "sigma =1\n",
    "alpha = 0.05\n",
    "z  = 1.645\n",
    "\n",
    "def pdf_func(xdata, mu, sigma):\n",
    "    val = np.exp(-np.power(xdata-mu,2)/(2*sigma**2))/(sigma *np.sqrt(2*np.pi))\n",
    "    return val\n",
    "\n",
    "fix, ax = plt.subplots()\n",
    "\n",
    "def pplot_gamma(mu, sigma, ax, z):\n",
    "    xdata = np.linspace(-5, 5, 1000)\n",
    "    xshade = xdata[xdata-mu/sigma>=-z]\n",
    "    ax.fill_between(xshade, pdf_func(xshade, mu, sigma), alpha=0.3 )\n",
    "    #xshade = xdata[xdata-mu/sigma<=-z]\n",
    "    #ax.fill_between(xshade, pdf_func(xshade, mu, sigma), alpha=0.3, color=\"blue\")\n",
    "    ax.plot(xdata, pdf_func(xdata, mu, sigma), label=r\"$\\mu=${},   $\\sigma=${}\".format(mu, sigma))\n",
    "    ax.set_ylim(0, 0.5) \n",
    "    ax.spines[\"top\"].set_visible(False)  \n",
    "    ax.spines[\"right\"].set_visible(False)\n",
    "    \n",
    "pplot_gamma(mu, sigma, ax, z)\n",
    "  \n",
    "ax.set_title(\"pdf of standard normal distribution\")\n",
    "plt.xticks([-4,0,4])\n",
    "plt.legend()  \n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 4.3-7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "$\\mu_Y = \\frac{80}{16}$\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###### nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "plt.figure(figsize=(4,6))\n",
    "\n",
    "for x in range(1,5):\n",
    "    for y in range(x+1,x+5):\n",
    "        plt.scatter(x,y, color=\"red\", edgecolor=\"black\",alpha=1)\n",
    "        plt.text(x+0.1,y+0.2, r\"$\\frac{1}{16}$\")\n",
    "        \n",
    "for x in range(1,5):\n",
    "    plt.text(x-0.1,-0.5, r\"$\\frac{1}{4}$\", color=\"red\", size=\"large\")\n",
    "    \n",
    "meany=0    \n",
    "    \n",
    "for y in range(2,9):\n",
    "    val =  4- np.abs(5-y)\n",
    "    plt.text(-1.5,y-0.13, r\"$\\frac{{{}}}{{16}}$\".format(val), color=\"red\", size=\"large\")\n",
    "    meany+=val*y\n",
    "    \n",
    "print(r\"$\\mu_Y = \\frac{{{}}}{{16}}$\".format(meany))\n",
    "\n",
    "plt.xticks(np.arange(1,5,1))\n",
    "plt.yticks(np.arange(2,9,1))\n",
    "plt.ylim(1,9)\n",
    "plt.xlim(0,5)\n",
    "plt.xlabel(\"x\", color=\"blue\")\n",
    "plt.ylabel(\"y\", color=\"blue\")\n",
    "plt.grid(True)\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQgAAAFzCAYAAADCE5f9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAWk0lEQVR4nO3dcWzcZ33H8fc3bVB8DVtZ3FmMkrtak1BjS5RdtjGaP2IHTZ2H+GPKIiLDlMnTKdIoZWNCmu4PYOMUZZMQE9oWoXkLki+OEDA0RZo20juLVWxlTl2qNmHSCInVgQZkQmB7hpR998c5wYR74nPt5/fc43xe0snO5dzfG2F/8vudL7G5OyIi3exKHSAi/UsDISJBGggRCdJAiEiQBkJEgjQQIhJ0f+qA9QYHB71SqaTO6Nny8jIPPPBA6oxNya05t17Is/nSpUvfcfeH7ry/rwaiUqkwPz+fOqNnc3NzHD58OHXGpuTWnFsv5NlsZte73a9LDBEJ0kCISJAGQkSCNBAiEqSBEJEgDYSIBGkgRCRIAyEiQRoIEQnSQIhIkAZCRII0ECISpIEQkSANhIgEaSBEJEgDISJBGggRCdJAiEiQBkJEgjQQIhKkgRApytWrMDUFR4+mLumZBkKkKMPDMD2dumJTNBAiEqSBEJEgDYRIUW7cgJMnYWEBTp1KXdOTvvrJWiI72r59cOZM6opN0RmEiATpDEKkKGbd73cvtmMTNBAiRenjIQjRJYZIkZaXoVqFCxdSl/REAyFSpNOn4dix1BU90yWGSFEuXoQDB2B1NXVJzzQQIkVptzuXGJcvw8AATEzArv4+iddAiBSl0ei8PXsWBgf7fhxAAyFSvBMnUhf0LOqEmdkfmNlLZvaimc2a2Z6YxxNJabbZZLRS4cj4OKOVCrPNZuqkLYs2EGb2BuB9wEF3HwXuA94V63giKc02m9RrNT5x/Tqr7nzi+nXqtVr2IxH7Iuh+YMDM7gdKwDciH08kiUa9zvTKCmPAbmAMmF5ZoVGvJy7bGvOIr+4ys6eABvC/wD+7+2SXx9SAGsDQ0FD1/Pnz0Xq229LSEnv37k2dsSm5NefSe2R8nFV3dq+77yawx4ynW61UWT0bGxu75O4Hf+o33D3KDXgd0AIeojOqnwfefbePqVarnpN2u506YdNya86ld6Rc9lbnxdS3by3wkXI5dVpPgHnv8jUZ8xLj7cDX3f3b7n4T+BzwtojHE0mm3mgwVSrRpnPm0AamSiXqt761mamY3+ZcBN5qZiU6lxhHgPmIxxNJ5vhk5+r5yXqdK4uLPLp/P41G4/b9uYo2EO7+rJl9BngOeAVYAD4Z63giqR2fnOT45CRzc3McPnw4dc62iPpCKXf/EPChmMcQkXj6/7WeIpKMBkJEgjQQIhKkgRCRIA2EiARpIEQkSAMhIkEaCBEJ0kCISJAGQkSCNBAiEqSBEJEgDYSIBGkgRCRIAyEiQRoIEQnSQIhIkAZC8nT1KkxNwdGjqUt6l2GzBkLyNDwM09OpKzYnw2YNhIgEaSBEJEgDIXm6cQNOnoSFBTh1KnVNbzJsjvrP3otEs28fnDmTumJzMmzWGYSIBOkMQvJk1v3+iD+tfssybNZASJ76+IsqKMNmXWJIvpaXoVqFCxdSl/Qus2YNhOTr9Gk4dix1xeZk1qxLDMnTxYtw4ACsrqYu6V2GzRoIyVO73Tldv3wZBgZgYgJ29fkJcYbNGgjJU6PReXv2LAwO9v0XGpBlswZC8nbiROqCzcuoOdqEmdmbzOz5dbfvmdn7Yx1PdpbZZpPRSoUj4+OMVirMNpupkzaUY/NGop1BuPt/AI8BmNl9wH8Bfx/reLJzzDab1Gs1pldWOAQ8c/06U7UaAMcnJ9PGBeTY3IuiLoKOAF9z9+sFHU8y1qjXmV5ZYQzYDYwB0ysrNOr1xGVhOTb3oqjnIN4FzHb7DTOrATWAoaEh5ubmCkrauqWlpax6IY/mK4uLHLrjvkNr9/dre47NPXH3qDfgNcB3gKGNHlutVj0n7XY7dcKm5dA8Ui57q/PC5Nu3FvhIuZw6LSjH5vWAee/yNVnEJcZvAM+5+38XcCzZAeqNBlOlEm3gJtAGpkol6re+TdiHcmzuRRGXGMcJXF6IdHPrSb0n63WuLC7y6P79NBqNvn6yL8fmnnQ7rdiuG1ACbgA/28vjdYkRX27NufW659lM4BIj6hmEu68A+2IeQ0Ti6f/XeopIMhoIEQnSQIhIkAZCRII0ECISpIEQkSANhIgEaSBEJEgDISJBGggRCdJAiEiQBkJEgjQQIhKkgRCRIA2EiARpIEQkSAMhcPUqTE3B0aOpS3qn5kJoIASGh2F6OnXF5qi5EBoIEQnSQIhIkAZC4MYNOHkSFhbg1KnUNb1RcyGK+tF70s/27YMzZ1JXbI6aC6EzCBEJ0hmEgFn3+zs//Kg/qbkQGgjp60/QIDUXQpcY0rG8DNUqXLiQuqR3ao5OAyEdp0/DsWOpKzZHzdHpEkPg4kU4cABWV1OX9E7NhdBACLTbnVPfy5dhYAAmJmBXn59cqrkQGgiBRqPz9uxZGBzs+09aQM0F0UDIj504kbpg89QcVf9PmIgkE3UgzOxBM/uMmX3VzK6Y2a/FPJ6EzTabjFYqHBkfZ7RSYbbZTJ10V7n1Qp7NG3L3aDfgU8Dvrb3/GuDBuz2+Wq16TtrtduqEnpybmfFHSiVvgf8QvAX+SKnk52ZmUqd1lVuve57N6wHz3u1ruNud23EDfgb4OmC9fowGIo6Rctlbndfx3b61wEfK5dRpXeXW655n83qhgYj5JOUw8G3g78zszcAl4Cl3X17/IDOrATWAoaEh5ubmIiZtr6WlpSx6rywucuiO+w6t3d+P/bn1Qp7NPem2GttxAw4CrwC/uvbrvwD+9G4fozOIOHL70y23Xvc8m9cjcAYR80nKl4GX3f3ZtV9/BviliMeTgHqjwVSpRBu4CbSBqVKJ+q3vy/eZ3Hohz+aedFuN7boB/wK8ae39DwN/frfH6wwinnMzMz5SLvsuMx8pl/v+ybPcet3zbL6Fop+k7ByTx4B54AXg88Dr7vZ4DUR8uTXn1uueZ3NoIKK+ktLdn6fzXISIZEivpBSRIA2EiARpIEQkSAMhIkEaCBEJ0kCISJAGQkSCNBAiEqSBEJEgDYSIBGkgRCRIAyEiQRoIEQnSQIhIkAZCRII0ECISpIGI4epVmJqCo0dTl/Qmt15Qc0E0EDEMD8P0dOqK3uXWC2ouiAZCRII0ECISpIGI4cYNOHkSFhbg1KnUNRvLrRfUXJCo/6r1PWvfPjhzJnVF73LrBTUXRGcQIhKkM4gYzLrf3/lhQv0nt15Qc0E0EDH08f/hXeXWC2ouiC4xYllehmoVLlxIXdKb3HpBzQXQQMRy+jQcO5a6one59YKaC6BLjBguXoQDB2B1NXVJb3LrBTUXRAMRQ7vdOZW8fBkGBmBiAnb18clabr2g5oJoIGJoNDpvz56FwcG+/yTIrhfUXBANREwnTqQu2JzcekHNkUUdCDO7Bnwf+BHwirsfjHk8EdleRZzjjLn7YztpHGabTUYrFY6MjzNaqTDbbKZO2lBuzbn1Qp7NG3L3u97A3wv+uo0e1/1juQYM9vr4arXq/e7czIw/Uip5C/yH4C3wR0olPzczkzotKLfm3Hrd82xeD5j3bl/D3e78iQfgHwX/T/BPgz8Bbht9zI8/lq8DzwGXgNpGj89hIEbKZW91XhN3+9YCHymXU6cF5dacW697ns3rhQbCvIeXf5phwK8DvwscBD4NTLvztbt/nP2Cu3/DzH4e+ALwpLt/8Y7H1IAawNDQUPX8+fO9nvwkcWR8nFV3dq+77yawx4ynW61UWXeVW3NuvZBn83pjY2OXvNvTAN1Wo9sN/M3gHwf/Kvhfgy+A/1nvH8+HgT+622N0BhFHbs259brn2bweW7jEeB/4JfB/Av9t8N1r9+8C/1r443gAeO26978EPHG3Y+UwEDlea+bWnFuve57N621lIP4EvBz4vUfDH8cw8JW120tAfaNj5TAQ7p1PhpFy2XeZ+Ui5nMUnQW7NufW659l8S2ggenoOoigHDx70+fn51Bk9m5ub4/Dhw6kzNiW35tx6Ic9mM+v6HET/v9ZTRJLRQIhIkAZCRII0ECISpIEQkSANhIgEaSBEJEgDISJBGggRCdJAiEiQBkJEgjQQIhKkgRCRIA2EiARpIEQkSAMhIkEaCBEJ0kDEcPUqTE3B0aOpS3qTWy/k2ZwhDUQMw8MwPZ26one59UKezRnSQIhIkAZCRII0EDHcuAEnT8LCApw6lbpmY7n1Qp7NGbo/dcCOtG8fnDmTuqJ3ufVCns0Z0hmEiATpDCIGs+7399EPKfoJufVCns0Z0kDEkNsnaW69kGdzhnSJEcvyMlSrcOFC6pLe5NYLeTZnRgMRy+nTcOxY6ore5dYLeTZnRpcYMVy8CAcOwOpq6pLe5NYLeTZnSAMRQ7vdOf29fBkGBmBiAnb18clabr2QZ3OGNBAxNBqdt2fPwuBg/3/i5tYLeTZnSAMR04kTqQs2J7deyLM5I9Fn18zuM7MFM9sxTzXPNpuMViocGR9ntFJhttlMnbSh3Jpz692x3D3qDfhD4BxwYaPHVqtV73fnZmb8kVLJW+A/BG+BP1Iq+bmZmdRpQbk159Z7p3a7nTph04B57/b12+3O7boBDwNPA+M7ZSBGymVvdV6mc/vWAh8pl1OnBeXWnFvvnXbSQMR+DuLjwAeB14YeYGY1oAYwNDTE3Nxc5KStubK4yKE77ju0dn+/tufWnFvvnZaWlrLo7Em31diOG/AO4K/W3j+MziCSya05t9477aQziJhPUj4OvNPMrgHngXEzm4l4vELUGw2mSiXawE2gDUyVStRvfdutD+XWnFvvjtZtNbb7xg46g3DvPIk2Ui77LjMfKZezePIst+bcetfbSWcQGogtyPETIbfm3Hrd82wODUQhL5Ry9zlgrohjicj20etTRSRIAyEiQRoIEQnSQIhIkAZCRII0ECISpIEQkSANhIgEaSBEJEgDISJBGggRCdJAiEiQBkJEgjQQIhKkgRCRIA2EiARpIEQkSAMRw9WrMDUFR4+mLulNbr1SGA1EDMPDMD2duqJ3ufVKYTQQIhKkgRCRIA1EDDduwMmTsLAAp06lrtlYbr1SmEL+2ft7zr59cOZM6ore5dYrhdEZhIgE6QwiBrPu93d+ylj/ya1XCqOBiCG3L6zceqUwusSIZXkZqlW4cCF1SW9y65VCaCBiOX0ajh1LXdG73HqlELrEiOHiRThwAFZXU5f0JrdeKYwGIoZ2u3PKfvkyDAzAxATs6uOTtdx6pTAaiBgajc7bs2dhcLD/v9hy65XCaCBiOnEidcHm5NYr0UX7o8LM9pjZl83sK2b2kpl9JNaxijbbbDJaqXBkfJzRSoXZZjN10oZybJb0Yp5B/AAYd/clM9sNPGNm/+ju/xbxmNHNNpvUazWmV1Y4BDxz/TpTtRoAxycn08YF5Ngs/SHaGYR3LK39cvfaLftX5DTqdaZXVhij8z9oDJheWaFRrycuC8uxWfpD1OcgzOw+4BLwi8BfuvuzXR5TA2oAQ0NDzM3NxUzasiuLixy6475Da/f3a3uOzbcsLS31feOdcmwOcvfoN+BBoA2M3u1x1WrV+91IueytzouTb99a4CPlcuq0oBybb2m326kTNi3HZmDeu3xNFvL9LHf/LjAHPFHE8WKqNxpMlUq0gZt0Vm+qVKJ+61uFfSjHZukP0S4xzOwh4Ka7f9fMBoC3A6djHa8ot57Ue7Je58riIo/u30+j0ejrJ/tybJb+EPM5iNcDn1p7HmIX8Gl33xF/E+j45CTHJyeZm5vj8OHDqXN6kmOzpBdtINz9BeAtsf77IhKfXlMrIkEaCBEJ0kCISJAGQkSCNBAiEqSBEJEgDYSIBGkgRCRIAyEiQRoIEQnSQIhIkAZCRII0ECISpIEQkSANhIgEaSBEJEgDEcPVqzA1BUePpi4R2RINRAzDwzA9nbpCZMs0ECISpIEQkSANRAw3bsDJk7CwAKdOpa4RedWi/ui9e9a+fXDmTOoKkS3TGYSIBOkMIgaz7vd79j/cXO4xGogYNASyQ+gSI5blZahW4cKO+GmDco/SQMRy+jQcO5a6QmRLdIkRw8WLcOAArK6mLhHZEg1EDO125xLj8mUYGICJCdilkzXJjwYihkaj8/bsWRgc1DhItjQQMZ04kbpAZEv0R5uIBEUbCDN7o5m1zeyKmb1kZk/FOlbRZptNRisVjoyPM1qpMNtspk4SiSLmJcYrwAfc/Tkzey1wycy+4O6XIx4zutlmk3qtxvTKCoeAZ65fZ6pWA+D45GTaOJFtFu0Mwt2/6e7Prb3/feAK8IZYxytKo15nemWFMWA3MAZMr6zQqNcTl4lsP/MCXhZsZhXgi8Cou3/vjt+rATWAoaGh6vnz56P3bMWR8XFW3dm97r6bwB4znm61UmX1bGlpib1796bO6FluvZBn89jY2CV3P/hTv+HuUW/AXuAS8FsbPbZarXq/GymXvdX52xa3by3wkXI5dVpP2u126oRNya3XPc9mYN67fE1G/S6Gme0GPgs03f1zMY9VlHqjwVSpRJvOmUMbmCqVqN967YPIDhLtSUozM2AauOLuH4t1nKLdeiLyyXqdK4uLPLp/P41GQ09Qyo4U8wziceA9wLiZPb92m4h4vMIcn5zkxWvXeLrV4sVr1zQOsmNFO4Nw92eAwL+cIiI50CspRSRIAyEiQRoIEQnSQIhIkAZCRII0ECISpIEQkSANhIgEaSBEJEgDISJBGggRCdJAiEiQBkJEgjQQIhKkgRCRIA2EiARpIEQkSAMhIkEaCBEJ0kCISJAGQkSCNBAiEqSBEJEgDYSIBGkgRCRIAyEiQRoIEQnSQIhIkAZCRII0ECISpIEQkSANhIgEaSBEJEgDISJBGggRCTJ3T91wm5l9G7ieumMTBoHvpI7YpNyac+uFPJvL7v7QnXf21UDkxszm3f1g6o7NyK05t17IszlElxgiEqSBEJEgDcTWfDJ1wKuQW3NuvZBnc1d6DkJEgnQGISJBGohXwcz+1sy+ZWYvpm7phZm90czaZnbFzF4ys6dSN23EzPaY2ZfN7CtrzR9J3dQLM7vPzBbM7ELqlu2ggXh1zgJPpI7YhFeAD7j7o8Bbgd83swOJmzbyA2Dc3d8MPAY8YWZvTdzUi6eAK6kjtosG4lVw9y8C/5O6o1fu/k13f27t/e/T+QR+Q9qqu/OOpbVf7l679fUTZmb2MPCbwN+kbtkuGoh7jJlVgLcAz6Yt2dja6frzwLeAL7h7vzd/HPgg8H+pQ7aLBuIeYmZ7gc8C73f376Xu2Yi7/8jdHwMeBn7FzEZTN4WY2TuAb7n7pdQt20kDcY8ws910xqHp7p9L3bMZ7v5dYI7+ft7nceCdZnYNOA+Mm9lM2qSt00DcA8zMgGngirt/LHVPL8zsITN7cO39AeDtwFfTVoW5+x+7+8PuXgHeBbTc/d2Js7ZMA/EqmNks8K/Am8zsZTObSt20gceB99D5U+35tdtE6qgNvB5om9kLwL/TeQ5iR3zrMCd6JaWIBOkMQkSCNBAiEqSBEJEgDYSIBGkgRCRIAyEiQRoIEQnSQMiWmPHLZrxgxh4zHjDjJTP69u9MyObohVKyZWZ8FNgDDAAvu3MqcZJsEw2EbJkZr6HzcuhV4G3u/ChxkmwTXWLIdvg5YC/wWjpnErJD6AxCtsyMf6DzV5wfAV7vznsTJ8k2uT91gOTNjN8BXnHnnBn3AV8yY9ydVuo22TqdQYhIkJ6DEJEgDYSIBGkgRCRIAyEiQRoIEQnSQIhIkAZCRII0ECIS9P87rCbSgSNXEQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 288x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###### nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "plt.figure(figsize=(4,6))\n",
    "\n",
    "for x in range(1,5):\n",
    "    for y in range(x+1,x+5):\n",
    "        plt.scatter(x,y, color=\"red\", edgecolor=\"black\",alpha=1, zorder=2)\n",
    "        plt.text(x+0.1,y+0.2, r\"$\\frac{1}{4}$\", color=\"red\")\n",
    "        \n",
    "\n",
    "    \n",
    "\n",
    "plt.xticks(np.arange(1,5,1))\n",
    "plt.yticks(np.arange(2,9,1))\n",
    "plt.ylim(1,9)\n",
    "plt.xlim(0,5)\n",
    "plt.xlabel(\"x\", color=\"blue\")\n",
    "plt.ylabel(\"y\", color=\"blue\")\n",
    "plt.grid(True)\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###### nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "plt.figure(figsize=(6,10))\n",
    "\n",
    "for x in range(1,5):\n",
    "    for y in range(x+1,x+5):\n",
    "        plt.scatter(x,y, color=\"red\", edgecolor=\"black\",alpha=1)\n",
    "        \n",
    "xval=np.array([1, 2, 3, 4])\n",
    "yval = xval+2.5\n",
    "ycond = np.array([3.5, 4.5, 5.5, 6.5])\n",
    "\n",
    "plt.plot(xval,yval,   linewidth=2, label=\"least squares\", color=\"orange\")\n",
    "\n",
    "\n",
    "    \n",
    "\n",
    "plt.xticks(np.arange(1,5,1))\n",
    "plt.yticks(np.arange(2,9,1))\n",
    "plt.ylim(1,9)\n",
    "plt.xlim(0,5)\n",
    "plt.xlabel(\"x\", color=\"blue\")\n",
    "plt.ylabel(\"y\", color=\"blue\")\n",
    "plt.legend()\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x2000 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###### nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "plt.figure(figsize=(6,10))\n",
    "\n",
    "for x in range(1,5):\n",
    "    for y in range(x+1,x+5):\n",
    "        plt.scatter(x,y, color=\"red\", edgecolor=\"black\",alpha=1)\n",
    "        \n",
    "xval=np.array([1, 2, 3, 4])\n",
    "yval = xval+2.5\n",
    "ycond = np.array([3.5, 4.5, 5.5, 6.5])\n",
    "\n",
    "plt.plot(xval,yval,   linewidth=2, label=\"least squares\", color=\"orange\")\n",
    "plt.scatter(xval,ycond,   linewidth=2, label=\"conditional mean\")\n",
    "\n",
    "\n",
    "    \n",
    "\n",
    "plt.xticks(np.arange(1,5,1))\n",
    "plt.yticks(np.arange(2,9,1))\n",
    "plt.ylim(1,9)\n",
    "plt.xlim(0,5)\n",
    "plt.xlabel(\"x\", color=\"blue\")\n",
    "plt.ylabel(\"y\", color=\"blue\")\n",
    "plt.legend()\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 4.2-10\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x2000 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###### nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "\n",
    "for x in range(0,10):\n",
    "    for y in range(x,10):\n",
    "        plt.scatter(x,y, color=\"red\", edgecolor=\"black\",alpha=1)\n",
    "        plt.text(x+0.1,y+0.2, r\"$\\frac{{1}}{{{}}}$\".format(10*(10-x)))\n",
    "        \n",
    "for x in range(0,10):\n",
    "    plt.text(x-0.1,-1.4, r\"$\\frac{1}{10}$\", color=\"red\", size=\"large\")\n",
    "    \n",
    "meany=0    \n",
    "\n",
    "val = 0\n",
    "for y in range(0,10):\n",
    "    val += 1/(10*(10-y))    \n",
    "    plt.text(-2,y-0.13, \"{:.4f}\".format(val), color=\"red\", size=\"large\")\n",
    "    \n",
    "plt.xticks(np.arange(0,10,1))\n",
    "plt.yticks(np.arange(0,10,1))\n",
    "plt.ylim(-0.5,10)\n",
    "plt.xlim(-0.5,10)\n",
    "plt.xlabel(\"x\", color=\"blue\")\n",
    "plt.ylabel(\"y\", color=\"blue\")\n",
    "plt.grid(True)\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.special import comb\n",
    "plt.figure(figsize=(6,6)) \n",
    "\n",
    "\n",
    "n=15\n",
    "pS=6/10\n",
    "pI=3/10\n",
    "pF=1/10\n",
    "\n",
    "x_range = []\n",
    "y_range = []\n",
    "for x in range(n+1):\n",
    "    for y in range(0,n-x+1):\n",
    "        plt.scatter(x,y,   color=(1,0,0,0.5))\n",
    "\n",
    "plt.xticks(np.arange(0,n+1,1))\n",
    "plt.yticks(np.arange(0,n+1,1))\n",
    "plt.title(r\"n={}, $p_S=${}, $p_I=${}, $p_F=${}\".format(n,pS,pI, pF))\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.special import comb\n",
    "plt.figure(figsize=(10,10)) \n",
    "\n",
    "\n",
    "meanx=0.49\n",
    "meany=0.22\n",
    "cov = -0.1578\n",
    "varx = 0.7099\n",
    "\n",
    "condmean = np.array([0.02, 0.08, 0.09, -0.06])\n",
    "\n",
    "x_range = np.array([-1,0,1,2])\n",
    "y_range = np.array([-1,0,1])\n",
    "\n",
    "pmf=np.array([[0.01, 0.04, 0.03, 0.1],\n",
    "             [0.08, 0.22, 0.24, 0.06],\n",
    "             [0.03, 0.12, 0.12, 0.04]])\n",
    "\n",
    "for i in range(len(x_range)):\n",
    "    for j in range(len(y_range)):\n",
    "        x = x_range[i]\n",
    "        y = y_range[j]\n",
    "        alpha = pmf[j,i]\n",
    "        plt.scatter(x,y, edgecolor=(0,0,1,max(min(alpha*5,0.9),0.01)), color=(1,0,0,max(min(alpha*5,0.9),0.01)))\n",
    "        \n",
    "\n",
    "xval=np.linspace(-2, 3, 10)\n",
    "yval = (xval-meanx)*cov/varx + meany\n",
    "plt.plot(xval,yval,   linewidth=2, label=\"least squares\")\n",
    "plt.plot(x_range,condmean,   linewidth=2, label= \"cond mean\")\n",
    "\n",
    "plt.scatter(meanx, meany, s=100 )   \n",
    "#plt.xticks(np.arange(0,n,1))\n",
    "#plt.yticks(np.arange(0,n,1))\n",
    "\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.legend()\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.4-4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###### nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "\n",
    "x = np.linspace(0, 1, 100)\n",
    "plt.fill_between(x, x**2, 1, alpha=0.5)\n",
    "plt.plot(x,x**2, color=\"red\", label=r\"$y=x^2$\")\n",
    "plt.text(0.7,0.4, r\"$y=x^2$\")\n",
    "plt.xticks([0,1])\n",
    "plt.yticks([1])\n",
    "\n",
    "plt.xlim(0,1)\n",
    "plt.ylim(0,1)\n",
    " \n",
    "\n",
    "\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###### nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "\n",
    "x = np.linspace(0, 1, 100)\n",
    "xval = np.linspace(1/2,1, 100)\n",
    "plt.fill_between(xval, np.maximum(xval**2, 1/2), 1, alpha=0.5)\n",
    "plt.plot(x,x**2, color=\"red\", label=r\"$y=x^2$\")\n",
    "plt.text(0.7,0.4, r\"$y=x^2$\")\n",
    "plt.xticks([1/2, 1], [r\"$\\frac{1}{2}$\", 1])\n",
    "plt.yticks([0,1/2, 1], [0, r\"$\\frac{1}{2}$\", 1])\n",
    "plt.xlim(0,1)\n",
    "plt.ylim(0,1)\n",
    "\n",
    " \n",
    "plt.vlines(1/2,0,1, linestyles='dashed', linewidth=0.7)    \n",
    "plt.hlines(1/2,0,1, linestyles='dashed', linewidth=0.7)    \n",
    "\n",
    "plt.xlabel(\"x\", color=\"blue\")\n",
    "plt.ylabel(\"y\", color=\"blue\")\n",
    "\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.4-14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAATUAAAEzCAYAAABQRpQZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAdF0lEQVR4nO3deZyNdcPH8c/vOjNmGGNfyr4TpVKWSpYSsoQxM/V0lxlCpLSombHTpjBJReJJCkmkQhjGzBh1q7u6VVpUSElKoVLUMHM9f5yeXm0YnHN+Z/m+X6/+GI7rfBOfrjPnnOsY13UREQkXju0BIiK+pKiJSFhR1EQkrChqIhJWFDURCSuKmoiElRNGzRgz1xiz1xjzfiAGiYicjuKcqc0Duvp5h4iIT5wwaq7r5gP7A7BFROS06XtqIhJWonx1IGPMYGAwQInYUhdUqVnXV4cWkQjmOVJAhS934rhFvF1Y+J3rupWPd3ufRc113dnAbICajc5275ixzFeHFpEIVX7XDpLSUylZpgxO9jpMixafn+jX+CxqIiK+VOHzbSSlpxDrcXDycuGcc4r164rzko5FwCagsTHmS2PMDae5VUTkuCrt2EryXf2ILRGNsyGv2EGDYpypua77P6czTkTkZFT59AP6jhxAifjSOLk50LDhSf16PfspIkHjjI/eJSk9hRLlyuJszD/poIGiJiJBotoHb9N35ACiKlfGyd8AdU/tFRSKmohYV+PdN0gYNZCo6tW8Z2i1a5/ysRQ1EbGq1tuv0WfMYDx16njP0KpXP63jKWoiYk2d/2yg9/ihOI0aeZ/lPOOM0z6moiYiVtT7dza9JgzDNGvmfZaz8nHfKFBsipqIBFzD/DX0vOdWOP98nJz1ULGiz46tqIlIQDXOWUG3SXdgWrfGyV4H5cr59PiKmogETNO1L3Ll5DTMpZdistZAmTI+vw9FTUQC4uxVz9M5cyRcdjnmlVegdGm/3I+iJiJ+13z5Qq54eCx0vRKzYjmUKuW3+9JVOkTEr85/YR4dnpiE26sXZvFiiInx6/0paiLiNy2fm03buZm4SUmYhQshOtrv96moiYjvuS5tFszgovmP4l57LebppyEqMLlR1ETEt1yXi+c9TOtFsyAlBfPkk+DxBOzuFTUR8R3X5dI5k7lw6VwYNAhmzQInsM9HKmoi4huuS4eZ93H+y/Nh2DB45JGABw0UNRHxhaIiLn9kAs1XLYbbb4fMTDDGyhS9Tk1ETospLOSKaaO9QcvIsBo00JmaiJwGU3iUrlPSaZKzEsaP9/5jMWigqInIKXKOHuHKB+6kUf4auO8+GDXK9iRAURORU+AcKaD7/bfT4LVsmDoVRoywPel3ipqInBRPwa/0vGc4dd/I8z7Decsttif9iaImIsUW9cthrpp4M7XfftX7GrQbb7Q96W8UNREplqjDh+g9fig13n0D5s6F/v1tT/pHipqInFD0oZ9IGDOYMz/cjHnmGbjuOtuTjklRE5HjivnpRxJGD6LqJ1swixZBcrLtScelqInIMcX8+D19Rw+kyo6tmCVLoE8f25NOSFETkX9U8vv9JI7sT8VdOzDLlkGPHrYnFYuiJiJ/U2r/tyRm9KfC17swK1ZA5862JxWboiYifxL33TckpadSbt/XmFWroGNH25NOiqImIr+L3/sVSWkpxP+4H5OVBW3b2p500hQ1EQGgzJ5dJKWnUvrwQZx166BNG9uTTomiJiKU3f05yWn9KHX0V5zsbLjwQtuTTpmiJhLhyn+xnaT0VEqaIpycHDjvPNuTTosuEikSwSp+9gnJaf0o6TE4ubkhHzRQ1EQiVqXtW0lOTyG2RDTOhjw4+2zbk3xCUROJQFU/2UJyWj9KlI7D2ZgPTZrYnuQzippIhDnjo3dIzOhPdIXyOPkboEED25N8SlETiSDV3n+LxJEDiKpSxRu0unVtT/I5RU0kQtR453X6jhqIp0YN70POWrVsT/ILRU0kAtR661X6jB2MU6+e9wytWjXbk/xGURMJc3XfyKP3+KE4jZvg5OVC1aq2J/mVoiYSxuq/ls1VE2/GnHMOTm4OVK5se5LfKWoiYarRhlX0uHc4XHABzvpsqFDB9qSAUNREwlCT9cvpNmkEps1FOGuzoFw525MCRlETCTNN1y6j6+Q0aN8ek7UGypSxPSmgFDWRMHLOyufoMnUkdLoCs3IlxMXZnhRwukqHSJg476X5dJx5L2637pgXlkJsrO1JVihqImGgxdK5tJ/9IG7v3pjFi6FECduTrFHUREJcy0WzaPvUNNzkZMyCBRAdbXuSVYqaSKhyXdrMf4yLFjwG112HeeopiNJfaf0OiIQi1+WSuQ/RavFs6N8f5swBj8f2qqCgqImEGtel3RMPcMGyeTB4MDz+ODh6IcP/0++ESCgpKqLDzHu9QbvlFpg1S0H7C52piYSKoiI6TR/POaufhxEjYMoUMMb2qqCjxIuEAFNYSOfMUd6gjRqloB2HztREgpwpPErXKek0yVkJEyfC2LEK2nEoaiJBzDl6hCsfuJNG+Wtg0iTIyLA9KegpaiJBylNQQPf7b6P+v9dDZibccYftSSFBURMJQp6CX+l59y3U/c8GeOwxGDbM9qSQoaiJBJmoXw7Ta8JN1Ny8CWbPhkGDbE8KKYqaSBCJPvwzvccNpfqWN71ve0pJsT0p5ChqIkGixM8/0WfMIM7c+i5m/ny49lrbk0KSoiYSBGIO/kDC6IFU3fYh5rnnIDHR9qSQpaiJWBb74wH6jryByjs/wSxdCr162Z4U0hQ1EYtKHthH4sj+VNy9E/PSS9Ctm+1JIU9RE7Ekbt9eEjP6U37vbu/nCXTqZHtSWFDURCyI++4bktNTKLN/L2b1amjf3vaksKGoiQRY/N6vSEpLIf7gAZw1a6BtW9uTwoqiJhJAZffsIik9hbjDP+GsWwetW9ueFHYUNZEAKbd7J0lpKZQqLMDJyYEWLWxPCkuKmkgAVPhiO4npqZQ0RTi5udC8ue1JYUsXiRTxs4qffULyXddT0mNw8vIUND9T1ET8qPK2D0lO60dMbAxO/gZo1sz2pLCnqIn4SdWP3yMpPYUS8aW9QWvc2PakiKCoifjBmR9uJjFjANEVK+JszIcGDWxPihiKmoiPVX/vTfqOuoGoM6p6z9Dq1LE9KaIoaiI+VHPzJhLGDMJTs6Y3aDVr2p4UcRQ1ER+p/dZGeo+7Ead+fZwNeVCtmu1JEUlRE/GBepty6DX+JpwmZ+Hk5ULVqrYnRSxFTeQ0NXh1LT3vvgVz7rk4uTlQqZLtSRFNURM5DY1yX6H7fbdBy5Y42eugfHnbkyKeoiZyis5a9xLdHrwTc/ElOGuzoGxZ25MERU3klDRbvYQuUzOgQwfM6lUQH297kvxGURM5Sc1XPEvnaWPgis7eK9bGxdmeJH+gq3SInITzX3yaDo/fj9u9B2bpEoiNtT1J/kJREymmC5Y8Sbs5k3ETEjCLFkGJErYnyT9Q1ESKodXCmVzy9HTcq6/2ftBwdLTtSXIMiprI8bguFz3zCG0WzoTrr8fMnQtR+msTzPRfR+RYXJe2czNpuXgODBgAs2eDx2N7lZyAoibyT1yX9rMm0eLFp2HIEJgxAxy9WCAUKGoif1VURMcZ93Deimfh1lth2jQwxvYqKSb9r0fkj4qK6DR9nDdod92loIUgnamJ/MYUFtI5cxRNs1+C0aPhnnsUtBCkqIkAztEjdJ2cTuO8V+Duu2HsWNuT5BQpahLxnCMFdJs0goavroUHH4S0NNuT5DQoahLRPAUF9Lj3Vuq9ngMPP+x9YkBCmqImEcvz6y9cdffN1HlzI8ycCUOH2p4kPqCoSUSKOnyIXhNuouY7r8OcOTBwoO1J4iOKmkSc6EM/0WfcEKq9/zZm3jzo18/2JPEhRU0iSomfD9JnzGDO3PouZuFCuOYa25PExxQ1iRgxB3+g76gbqLL9I8zixdC3r+1J4geKmkSE2B/2kzjyBip9sQ2zbBn07Gl7kviJoiZhr+SBfSSO7E/F3TsxL78MXbvaniR+pKhJWIvbt5fEjFTK7/3K+3kCnTrZniR+pqhJ2Cr97dckpadQ5sC3mNWroX1725MkABQ1CUvx3+wmKT2F+IPf42RlwSWX2J4kAaKoSdgpu2cXSWn9iPv1EE52NrRqZXuSBJCiJmGl3JefkZyeSsnCApz166FFC9uTJMAUNQkbFT7fRlJ6KrEOOLm50Ly57Uliga58K2Gh0o6tJN/Vj9hoD86GPAUtgilqEvKqfPoBSWkpxJSKxcnfAE2b2p4kFilqEtKqbn2PxIxUSpQt4w1ao0a2J4llipqErGofvE1iRn+iK1XC2ZgP9evbniRBQFGTkFT9vf+QMGogUdWrec/Qate2PUmChKImIafWf/9NwuhBeGrX9j4pUKOG7UkSRBQ1CSm138yn97ghOA0beoN25pm2J0mQUdQkZNTblEOvCcMwTZvi5OVClSq2J0kQUtQkJDTYmEXPu2/BnHceTs56qFjR9iQJUoqaBL1Gua/Q/f7bMa1a4WSvg/LlbU+SIKaoSVBruvZFuj14J6ZtW8zaLChTxvYkCXKKmgSts1cvoXPmSOh4GWbVKihd2vYkCQGKmgSl5iue5YppY6BzF8yK5VCqlO1JEiJ0lQ4JOucvm0eHWZNwe/TELF0CMTG2J0kI0ZmaBJULF8/2Bq1vX8wLS/0WtI4dO7Ju3ToAxowZw/Dhw0/6GFu2bOGSP1xR97///S+XXXaZzzbKqdGZmgSN1gtmcPEzj+Becw1m/nyI8t8fz4kTJzJu3Dj27t3L5s2bWb58+Z9+/tJLL+XgwYN/+3VTp06l028f3tKsWTO2b99OYWEhHo+HESNGkJmZ6bfNUjyKmtjnulw872FaL5oF/fph5s4Fj8evd9muXTtc1+Whhx4iLy8Pz1/ub+PGjSc8huM4NGvWjA8++IBPP/2UWrVq0UJX2rVOURO7XJdL/3cKFy55EgYOhCeeAMf/3xXZsmULe/bsoVKlSsTHx//t54tzpgbQpk0bXnvtNWbOnMmaNWv8ulmKR1ETe1yXDo/fx/kvzYebboJHHw1I0Pbs2cO//vUvXn75ZYYPH05WVhZdunT5022Kc6YG3qilpqYybNgwqlev7o+5cpL0RIHYUVTEZY9O8AbtttvgsccCErRDhw6RkJBAZmYmZ511FmPHjmXChAmnfLwmTZoQExNDenq670bKadGZmgScKSyk08NjOTvrBUhPh0mTwJiA3HepUqXYtGnT71+3a9fuT1+frOnTpzNp0iTi4uJ8MU98QGdqElCm8ChdpmZ4gzZuXECD5kvbt2+nSZMmHD58mJSUFNtz5A90piYB4xw9QtfJaTTOWwX33gujR9uedMrq16/P1q1bbc+Qf6CoSUA4RwroNmkEDV9dC1OmwJ132p4kYUpRE7/zFBTQ497h1Hs9F6ZPh1N49b5IcSlq4leeX3/hqok3U+etjfD44zBkiO1JEuYUNfGbqMOH6DXhJmq+8zo8+SQMGGB7kkQARU38IvrQT/QZeyPVPvgv5umn4frrbU+SCKGoic+V+PkgCaMHccbH72GefRauvtr2JIkgipr4VMzBH+g7agBVdnyMef55SEiwPUkijKImPhP7w34SRw6g0hfbMcuWQY8etidJBFLUxCdKHthHUkYqFfZ8gVm+HP7yBnGRQFHU5LTF7fuGpPT+lPv2K8zKlXD55bYnSQRT1OS0lN67h+T0FOJ/2IdZswbatbM9SSKcoianrMzXX5KUnkrpn3/AWbsWLrrI9iQRRU1OTdndn5OcnkKpgsM42dnQsqXtSSKAoianoPyuHSSlp1Ky6ChObi6cd57tSSK/U9TkpFTc+SmJGanEehycDXlw9tm2J4n8iS4SKcVWaftWktP6EVsiWkGToKWoSbFU+eR9ktP6USKuFE7+BjjrLNuTRP6RoiYndMZH75KUkUp0+XI4G/OhYUPbk0SOSVGT46r2/lv0HTmAqCpVvEGrW9f2JJHjUtTkmGq8+wYJowcRVb2a9yFnrVq2J4mckKIm/6jW26/RZ8xgPHXqeIOmD+qVEKGoyd/U+c8Geo8fitOokfdZzjPOsD1JpNgUNfmTev/OpteEYZhmzXByc6ByZduTRE6Koia/a5i/mp733AotWuDkrIeKFW1PEjlpipoA0DhnBd3vvwPTujXOurVQrpztSSKnRFETmq59kSsnp0G7dpisNVCmjO1JIqdMUYtw57yymM6ZI+GyyzGvvAKlS9ueJHJaFLUIdu7LC+g0fRx0vRKzYjmUKmV7kshp01U6IlSLpU/RfvYDuL16YRYvhpgY25NEfEJRi0AtFz1B26cewk1M9H4uZ3S07UkiPqOoRRLXpc2CGVw0/1Hca6/1fnJ6lP4ISHjRn+hI4bpcPO9hWi+aBSkpmCefBI/H9ioRn1PUIoHrcumcyVy4dC4MHgyPPw6OniOS8KSohTvXpcPM+zj/5flw883wyCNgjO1VIn6jqIWzoiIuf3QCzV9ZDLffDpmZCpqEPT0GCVOmsJArpo32Bm3kSAVNIobO1MKQKTxKl6kZnLV+BUyYAOPGKWgSMRS1MOMcPcKVD95Fow2r4b77YNQo25NEAkpRCyPOkQK6338HDV5bB1OnwogRtieJBJyiFiY8Bb/S857h1H0jz/sM5y232J4kYoWiFgaifjnMVRNvpvbbr8KsWXDjjbYniVijqIW4qMOH6D1+KDXefQPmzoX+/W1PErFKUQth0Yd+ImHMYM78cDPmmWfguutsTxKxTlELUTE//UjC6EFU/WQLZtEiSE62PUkkKChqISjmx+/pO3ogVXZsxSxZAn362J4kEjQUtRBT8vv9JI7sT8VdOzDLlkGPHrYniQQVRS2ElNr/LYkZ/anw9S7MihXQubPtSSJBR1ELEXHffUNSeirl9n2NWbUKOna0PUkkKClqISB+71ckpaUQf/AAJisL2ra1PUkkaClqQa7Mnl0kpadS+vBBnLVroU0b25NEgpqiFsTK7v6c5PQUSh35BSc7Gy680PYkkaCnqAWp8l9sJyk9lZKmCCc3F8491/YkkZCgi0QGoYqffcLVd11PSY/ByctT0EROgqIWZCpv/4jktH7ExMbg5G+AZs1sTxIJKYpaEKn6yRaS0lIoEV/aG7TGjW1PEgk5ilqQOOOjd0jM6E90hfLeoDVoYHuSSEhS1IJA9S1vkThyAFFVqniDVreu7UkiIUtRs6zm5k0kjB6Ip0YNnI35UKuW7UkiIU1Rs6jWW6/Se9yNOPXqec/QqlWzPUkk5ClqltR9I4/e44fiNG6Ck5cLVavaniQSFhQ1C+q/ls1VE2/GnHMOTm4OVK5se5JI2FDUAqxh/mp63HsrtGiBsz4bKlSwPUkkrChqAdRk/XK6338Hpk0bnOx1UK6c7UkiYUdRC5CmWS/QdXIatG+PyVoD8fG2J4mEJUUtAM5Z+RxdMkdBpyswK1dCXJztSSJhS1fp8LPzXppPx5n34nbrjnlhKcTG2p4kEtYUNT+6YMmTtJszGbd3b8xzz0FMjO1JImFPUfOTlotm0fapabjJyZgFCyA62vYkkYigqPma69Jm/mNctOAxuO46zFNPQZR+m0UCRX/bfMl1ueSpabR67gkYMABmzwaPx/YqkYiiqPmK69Ju9oNc8MJTMGQIzJgBjp5cFgk0Rc0Xioro8Ph9nP/yAhg+HB5+GIyxvUokIilqp6uoiE7Tx3PO6udhxAiYMkVBE7FIj49OgykspHPmKG/QRo9W0ESCgM7UTpEpPErXKek0yVkJEyfCuHG2J4kIitopcY4e4cpJI2i0MQsmTYKMDNuTROQ3itpJ8hQU0P2+W6m/KQceeghuv932JBH5A0XtJHh+/YWr7r6FOm/mw2OPwbBhtieJyF8oasUU9cthek24iZqbN3lfVDtokO1JIvIPFLViiD78M73HDaX6e//xvu0pJcX2JBE5BkXtBEr8/BN9xgzizK3vet+Yfu21tieJyHEoascRc/AHEkYPpOq2D72XDkpMtD1JRE5AUTuG2B8P0HfkDVTe+Qlm6VLo1cv2JBEpBkXtH5Q8sI/Ekf2puHsn5qWXoFs325NEpJgUtb+I27eXxIz+lN+72/t5Ap062Z4kIidBUfuDuO++ITk9hTL792JWr4b27W1PEpGTpKj9Jn7vVySlpRB/8ADOmjXQtq3tSSJyChQ1oOyeXSSlpxB3+CecdeugdWvbk0TkFEV81Mrt3klSWgqlCgtwcnKgRQvbk0TkNER01Cp8sZ3E9FRKmiKc3Fxo3tz2JBE5TRF7kciKn31C8l3XU9JjcPLyFDSRMBGRUau87UOS0/oRExuDk78BmjWzPUlEfCTiolb14/dISk+hRHxpb9AaN7Y9SUR8KKKiduaHm0nMGEB0xYo4G/OhQQPbk0TExyImatXfe5O+o24g6oyq3jO0OnVsTxIRP4iIqNXcvImEMYPw1KzpDVrNmrYniYifhH3Uar+1kd7jbsSpXx9nQx5Uq2Z7koj4UVhHrd6mHHqNvwmnyVk4eblQtartSSLiZ2EbtQavrqXn3bdgzj0XJzcHKlWyPUlEAiAso9YobxXd77sNWrbEyV4H5cvbniQiARJ2UTsr+yW6PTACc9HFOGuzoGxZ25NEJIDCKmrN1iyly5QM6NABs2Y1xMfbniQiARY2UWu+4lk6PzQaOnfxXrE2Ls72JBGxICyu0nH+i0/T4fH7cbv3wLywFGJibE8SEUtC/kztgiVPeoOWkIBZ9oKCJhLhQvpMrdXCmVzy9HTcq6/GzJ8P0dG2J4mIZaEZNdflomceoc3CmXD99Zi5cyEqNP9VRMS3Qq8ErkvbuZm0XDwHBgyA2bPB47G9SkSCRGhFzXVpP2sSLV58GoYMgRkzwAn5bwuKiA+FThGKiug44x5v0G69FWbOVNBE5G9CowpFRXSaPo7zli+EtDSYNg2Msb1KRIJQ0D/8NIWFdM4cRdPsl2DMGLj7bgVNRI4pqKNmCo/SdXI6TXJXemM2dqztSSIS5II2as6RAro9cCcNN2bBAw9AerrtSSISAoIyap6CAnrceyv1Xs/xfv/stttsTxKREBF0UfP8+gtX3X0zdd7c6H2Gc+hQ25NEJIQEVdSiDh+i14SbqPnO6zBnDgwcaHuSiISYoIla9KGf6DNuCNXefxszbx7062d7koiEoKCIWomfD9JnzGDO3PouZuFCuOYa25NEJERZj1rMwR/oO+oGqmz/CLN4MfTta3uSiIQwq1GL/WE/iSNvoNIX2zDLlkHPnjbniEgYsBa1kgf2kTiyPxV378S8/DJ07WprioiEEStRi9u3l8SMVMrv/cr7eQKdOtmYISJhKOBRK/3t1ySlp1DmwLeY1auhfftATxCRMBbQqMV/s5uk9BTiD36Pk5UFl1wSyLsXkQgQsKiV3bOLpLR+xP16CCc7G1q1CtRdi0gECUjUyn35GcnpqZQsLMBZvx5atAjE3YpIBPJ71Cp8vo2k9FRiHXByc6F5c3/fpYhEML9e+bbSjq0k39WP2GgPzoY8BU1E/M5vUavy6QckpaUQUyoWJ38DNG3qr7sSEfmdcV3X5wetV6u++9H33xFdrhxObg7Ur+/z+xCRyGOMedt13QuPdxu/nKmV372T6EqVcDbmK2giElB+eaLAREd7H3LWqOGPw4uIHJNfHn4aYw4CH/v8wCIS6Rq7rht/vBv46yUdH5/oca+IyMkyxrx1otuExocZi4gUk6ImImHFX1Gb7afjikhkO2Fb/PJEgYiILXr4KSJhxadRM8Z0NcZ8bIzZZozJ8OWxRSRyGWPmGmP2GmPeP9FtfRY1Y4wHmAFcCTQF/scYozd8iogvzAOK9UEmvjxTawVsc113h+u6BcBzQC8fHl9EIpTruvnA/uLc1pdRqw7s+sPXX/72YyIiAePLqJl/+DE9tSoiAeXLqH0J1PzD1zWAr3x4fBGRE/Jl1N4EGhpj6hpjSgDXAMt9eHwRkRPyWdRc1z0K3AxkAR8Bz7uu+4Gvji8ikcsYswjYBDQ2xnxpjLnhmLfVOwpEJJzoHQUiElYUNREJK4qaiIQVRU1EwoqiJiJhRVETkbCiqIlIWFHURCSs/B87+0tcxj+i4AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###### nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "\n",
    "x = np.linspace(0, 1, 100)\n",
    "plt.fill_between(x, x, 1, alpha=0.5)\n",
    "plt.plot(x,x, color=\"red\", label=r\"$y=x^2$\")\n",
    "plt.text(0.6,0.5, r\"$x=y$\")\n",
    "plt.xticks([0,1])\n",
    "plt.yticks([1])\n",
    "\n",
    "plt.xlim(0,1)\n",
    "plt.ylim(0,1)\n",
    " \n",
    "\n",
    "\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###### nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "x = np.linspace(0, 1, 100)\n",
    "plt.fill_between(x, x, 1, alpha=0.5)\n",
    "plt.text(0.6,0.5, r\"$x=y$\")\n",
    "plt.xticks([0,1])\n",
    "plt.yticks([1])\n",
    "\n",
    "plt.xlim(0,1)\n",
    "plt.ylim(0,1)\n",
    "\n",
    "meanx=8/15\n",
    "meany=4/5\n",
    "sigma2x=11/225\n",
    "cov=4/225\n",
    "\n",
    "xval = np.linspace(-0.1, 1.1, 100)\n",
    "yval = (xval-meanx)*cov/sigma2x + meany\n",
    "plt.plot(xval,yval,   linewidth=2, label=\"least squares line\", color=\"g\")\n",
    "\n",
    "\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.4-18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###### nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "\n",
    "y = np.linspace(0, 4, 100)\n",
    "plt.fill_betweenx(y, y, y+2, alpha=0.5)\n",
    "\n",
    "plt.xlim(0,6)\n",
    "plt.ylim(0,4)\n",
    "\n",
    " \n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###### nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "plt.figure(figsize=(6,4))\n",
    "\n",
    "y = np.linspace(0, 4, 100)\n",
    "plt.fill_betweenx(y, y, y+2, alpha=0.5)\n",
    "\n",
    "x=np.linspace(0,6,100)\n",
    "plt.plot(x, x-1, color=\"green\")\n",
    "\n",
    "plt.xlim(0,6)\n",
    "plt.ylim(0,4)\n",
    "\n",
    " \n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "###### nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "plt.figure(figsize=(6,4))\n",
    "\n",
    "y = np.linspace(0, 4, 100)\n",
    "plt.fill_betweenx(y, y, y+2, alpha=0.5)\n",
    "\n",
    "x=np.linspace(0,6,100)\n",
    "\n",
    "def condmean(x):\n",
    "    f1=lambda x: x/2\n",
    "    f2=lambda x: x-1\n",
    "    f3=lambda x: (x+2)/2\n",
    "    z=np.piecewise(x, [x<2, (x>=2)&(x<=4), (x>=4)], [f1, f2, f3])\n",
    "    return z\n",
    "\n",
    "plt.plot(x, condmean(x), color=\"green\")\n",
    "\n",
    "plt.xlim(0,6)\n",
    "plt.ylim(0,4)\n",
    "\n",
    " \n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.1-4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "# library\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "plt.rcParams[\"figure.figsize\"] = (15, 6)\n",
    "\n",
    "\n",
    "# generate data\n",
    "data = np.array([320, 326, 325, 318, 322, 320, 329, 317, 316, 331,\n",
    "                 320, 320, 317, 329, 316, 308, 321, 319, 322, 335,\n",
    "                 318, 313, 327, 314, 329, 323, 327, 323, 324, 314,\n",
    "                 308, 305, 328, 330, 322, 310, 324, 314, 312, 318,\n",
    "                 313, 320, 324, 311, 317, 325, 328, 319, 310, 324])\n",
    "\n",
    "# compute empirical pmf\n",
    "def epmf(data):\n",
    "    erange_x, counts = np.unique(data, return_counts=True)\n",
    "    epmf_values = counts\n",
    "    return epmf_values, erange_x\n",
    "\n",
    "epmf_values, erange_x = epmf(data)\n",
    "\n",
    "# plot \n",
    "plt.axhline(y=0, color='k')\n",
    "plt.xticks(erange_x)\n",
    "\n",
    "plt.bar(erange_x, epmf_values, width=1, color='#039be5', edgecolor='black', linewidth=1)\n",
    "\n",
    "mean = np.mean(data)\n",
    "std = np.sqrt(np.var(data, ddof=1))\n",
    "\n",
    "plt.scatter(mean, 0, color=\"red\", label=\"mean\", zorder=3, s=50)\n",
    "plt.vlines([mean-std, mean+std], -0.3,3.5,  label=\"1 std from mean\", zorder=3)\n",
    "plt.vlines([mean-2*std, mean+2*std], -0.3,3.5,  linestyle=\"dashed\", label=\"2 std from mean\", zorder=3)\n",
    "\n",
    "plt.legend(loc='upper left')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([305, 308, 308, 310, 310, 311, 312, 313, 313, 314, 314, 314, 316,\n",
       "       316, 317, 317, 317, 318, 318, 318, 319, 319, 320, 320, 320, 320,\n",
       "       320, 321, 322, 322, 322, 323, 323, 324, 324, 324, 324, 325, 325,\n",
       "       326, 327, 327, 328, 328, 329, 329, 329, 330, 331, 335])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sort(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "320.1"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.7499055171014"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(np.var(data, ddof=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50,)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams[\"figure.figsize\"] = (10, 6)\n",
    "\n",
    "N=100 # total number of samples\n",
    "# intsize the number of class intervals\n",
    " \n",
    "# generate data\n",
    "data = np.array([320, 326, 325, 318, 322, 320, 329, 317, 316, 331,\n",
    "                 320, 320, 317, 329, 316, 308, 321, 319, 322, 335,\n",
    "                 318, 313, 327, 314, 329, 323, 327, 323, 324, 314,\n",
    "                 308, 305, 328, 330, 322, 310, 324, 314, 312, 318,\n",
    "                 313, 320, 324, 311, 317, 325, 328, 319, 310, 324])\n",
    "\n",
    "\n",
    "# Add the histogram\n",
    "plt.hist(data, bins='auto', color='#039be5', edgecolor='black', linewidth=1)\n",
    "\n",
    "# Add the mean and variances\n",
    "mean = np.mean(data)\n",
    "std = np.sqrt(np.var(data, ddof=1))\n",
    "plt.scatter(mean, 0, color=\"red\", label=\"mean\", zorder=3, s=50)\n",
    "plt.vlines([mean-std, mean+std], -1,10,   label=\"1 std from mean\", linewidth=1.2, zorder=3)\n",
    "plt.vlines([mean-2*std, mean+2*std], -1,10,  linestyle=\"dashed\", linewidth=1.2, label=\"2 std from mean\", zorder=3)\n",
    "\n",
    "plt.legend(loc='upper left')\n",
    "plt.show();\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[313.3500944828986, 326.84990551710143, 306.6001889657972, 333.59981103420284]"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[mean-std, mean+std, mean-2*std, mean+2*std]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "31\n",
      "48\n"
     ]
    }
   ],
   "source": [
    "print(np.sum([(mean-std<=data) & (data<=mean+std)]))\n",
    "print(np.sum([(mean-2*std<=data) & (data<=mean+2*std)]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([ True,  True,  True,  True,  True,  True, False,  True,  True,\n",
       "        False,  True,  True,  True, False,  True, False,  True,  True,\n",
       "         True, False,  True, False, False,  True, False,  True, False,\n",
       "         True,  True,  True, False, False, False, False,  True, False,\n",
       "         True,  True, False,  True, False,  True,  True, False,  True,\n",
       "         True, False,  True, False,  True])]"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[(mean-std<=data) & (data<=mean+std)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.2-2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([320, 326, 325, 318, 322, 320, 329, 317, 316, 331, 320, 320, 317,\n",
       "       329, 316, 308, 321, 319, 322, 335, 318, 313, 327, 314, 329, 323,\n",
       "       327, 323, 324, 314, 308, 305, 328, 330, 322, 310, 324, 314, 312,\n",
       "       318, 313, 320, 324, 311, 317, 325, 328, 319, 310, 324])"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams[\"figure.figsize\"] = (10, 6)\n",
    "\n",
    "N=100 # total number of samples\n",
    "# intsize the number of class intervals\n",
    " \n",
    "# generate data\n",
    "data1 = np.array([1.03, 1.03, 1.06, 1.02, 1.03, 1.03, 1.03, 1.02, 1.03, 1.03,\n",
    "                  1.06, 1.04, 1.05, 1.03, 1.04, 1.03, 1.05, 1.06, 1.04, 1.04,\n",
    "                  1.03, 1.04, 1.04, 1.06, 1.03, 1.04, 1.05, 1.04, 1.04, 1.02,\n",
    "                  1.03, 1.05, 1.05, 1.03, 1.04, 1.03, 1.04, 1.04, 1.03, 1.04,\n",
    "                  1.03, 1.04, 1.04, 1.04, 1.05, 1.04, 1.04, 1.03, 1.03, 1.05,\n",
    "                  1.04, 1.04, 1.05, 1.04, 1.03, 1.03, 1.05, 1.03, 1.04, 1.05,\n",
    "                  1.04, 1.04, 1.04, 1.05, 1.03, 1.04, 1.04, 1.04, 1.04, 1.03,\n",
    "                  1.05, 1.05, 1.05, 1.03, 1.04])\n",
    "\n",
    "\n",
    "data2 = np.array([1.29, 1.10, 1.28, 1.29, 1.23, 1.20, 1.31, 1.25, 1.13, 1.26,\n",
    "                  1.19, 1.33, 1.24, 1.20, 1.26, 1.24, 1.11, 1.14, 1.15, 1.15,\n",
    "                  1.19, 1.26, 1.14, 1.20, 1.20, 1.20, 1.24, 1.25, 1.28, 1.24,\n",
    "                  1.26, 1.20, 1.30, 1.23, 1.26, 1.16, 1.34, 1.10, 1.22, 1.27.\n",
    "                  1.21, 1.09, 1.23, 1.03, 1.32, 1.21, 1.23, 1.34, 1.19, 1.18,\n",
    "                  1.20, 1.20, 1.13, 1.43, 1.19, 1.05, 1.16, 1.19, 1.07, 1.21,\n",
    "                  1.36, 1.21, 1.00, 1.23, 1.22, 1.13, 1.24, 1.10, 1.18, 1.26,\n",
    "                  1.12, 1.10, 1.19, 1.10, 1.24])\n",
    "\n",
    "\n",
    "# Add the histogram\n",
    "plt.hist(data, bins='auto', color='#039be5', edgecolor='black', linewidth=1)\n",
    "\n",
    "# Add the mean and variances\n",
    "mean = np.mean(data)\n",
    "std = np.sqrt(np.var(data, ddof=1))\n",
    "plt.scatter(mean, 0, color=\"red\", label=\"mean\", zorder=3, s=50)\n",
    "plt.vlines([mean-std, mean+std], -1,10,   label=\"1 std from mean\", linewidth=1.2, zorder=3)\n",
    "plt.vlines([mean-2*std, mean+2*std], -1,10,  linestyle=\"dashed\", linewidth=1.2, label=\"2 std from mean\", zorder=3)\n",
    "\n",
    "plt.legend(loc='upper left')\n",
    "plt.show();\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# set up the figure\n",
    "fig, ax = plt.subplots(1,1, figsize=(10,5))\n",
    "\n",
    "# generate data\n",
    "data1 = np.array([1.03, 1.03, 1.06, 1.02, 1.03, 1.03, 1.03, 1.02, 1.03, 1.03,\n",
    "                  1.06, 1.04, 1.05, 1.03, 1.04, 1.03, 1.05, 1.06, 1.04, 1.04,\n",
    "                  1.03, 1.04, 1.04, 1.06, 1.03, 1.04, 1.05, 1.04, 1.04, 1.02,\n",
    "                  1.03, 1.05, 1.05, 1.03, 1.04, 1.03, 1.04, 1.04, 1.03, 1.04,\n",
    "                  1.03, 1.04, 1.04, 1.04, 1.05, 1.04, 1.04, 1.03, 1.03, 1.05,\n",
    "                  1.04, 1.04, 1.05, 1.04, 1.03, 1.03, 1.05, 1.03, 1.04, 1.05,\n",
    "                  1.04, 1.04, 1.04, 1.05, 1.03, 1.04, 1.04, 1.04, 1.04, 1.03,\n",
    "                  1.05, 1.05, 1.05, 1.03, 1.04]).astype(float)\n",
    "\n",
    "\n",
    "data2 = np.array([1.29, 1.10, 1.28, 1.29, 1.23, 1.20, 1.31, 1.25, 1.13, 1.26,\n",
    "                  1.19, 1.33, 1.24, 1.20, 1.26, 1.24, 1.11, 1.14, 1.15, 1.15,\n",
    "                  1.19, 1.26, 1.14, 1.20, 1.20, 1.20, 1.24, 1.25, 1.28, 1.24,\n",
    "                  1.26, 1.20, 1.30, 1.23, 1.26, 1.16, 1.34, 1.10, 1.22, 1.27,\n",
    "                  1.21, 1.09, 1.23, 1.03, 1.32, 1.21, 1.23, 1.34, 1.19, 1.18,\n",
    "                  1.20, 1.20, 1.13, 1.43, 1.19, 1.05, 1.16, 1.19, 1.07, 1.21,\n",
    "                  1.36, 1.21, 1.00, 1.23, 1.22, 1.13, 1.24, 1.10, 1.18, 1.26,\n",
    "                  1.12, 1.10, 1.19, 1.10, 1.24]).astype(float)\n",
    "\n",
    "\n",
    "\n",
    "def percentile(data, p):\n",
    "    \"\"\"\n",
    "    Compute the percentiles the way we defined in class \n",
    "    data : array of size N \n",
    "    p : percentile\n",
    "    \"\"\"\n",
    "    data = np.sort(data, axis=0)\n",
    "    rank = int(p * (data.shape[0] + 1) - 1) # the rank\n",
    "    assert rank > 0, \"the rank does not exist\" \n",
    "    alpha = p * (data.shape[0] + 1) - 1 - rank # the fractional part\n",
    "    return data[rank] + alpha * (data[rank + 1] - data [rank])\n",
    "\n",
    "def box_plot(ax, data, width=0.4, showout = True, position = np.array([0.4]), \n",
    "             textloc=np.array([0.8]), label = \"\"):\n",
    "    \"\"\"\n",
    "    ax : matplotlib ax\n",
    "    data : the data \n",
    "    width : box width\n",
    "    showout : show the outliers   \n",
    "    position: the y axis of the box plot\n",
    "    \"\"\"\n",
    "    # compute the five number summary \n",
    "    minim = np.min(data)\n",
    "    maxim = np.max(data)\n",
    "    q1 = percentile(data, 0.25)\n",
    "    q2 = np.median(data)\n",
    "    q3 = percentile(data, 0.75)\n",
    "\n",
    "    # interquartile range\n",
    "    iqr = q3 - q1\n",
    "\n",
    "    # inner fences\n",
    "    left_innerfence = q1 - 1.5 * iqr\n",
    "    right_innerfence = q3 + 1.5 * iqr\n",
    "\n",
    "    # compute outliers \n",
    "    outliers = []\n",
    "    \n",
    "    # whiskers\n",
    "    if showout==True:\n",
    "        outliers = data[np.logical_or(data <left_innerfence, data >= right_innerfence)]\n",
    "        low_whisker = np.min(data[data >= left_innerfence])\n",
    "        high_whisker = np.max(data[data <= right_innerfence])\n",
    "    else:\n",
    "        low_whisker = np.min(data)\n",
    "        high_whisker = np.max(data)\n",
    "\n",
    "\n",
    "\n",
    "    stats = [{'iqr': iqr,\n",
    "              'whishi': high_whisker,\n",
    "              'whislo': low_whisker,\n",
    "              'fliers': outliers,\n",
    "              'q1': q1,\n",
    "              'med': q2,\n",
    "              'q3': q3}]\n",
    "\n",
    "    # add the box plot\n",
    "    flierprops = dict(markerfacecolor='black', markersize=5)\n",
    "    ax.bxp(stats, vert = False, widths=width, positions = position, \n",
    "           flierprops=flierprops, showfliers=showout)\n",
    "\n",
    "    # add Tukey's fences\n",
    "    if showout==True:\n",
    "        ax.vlines(q1-1.5*iqr, position-0.2,position+0.2, linestyle=\"dashed\", linewidth=1)\n",
    "        ax.vlines(q3+1.5*iqr, position-0.2,position+0.2, linestyle=\"dashed\", linewidth=1)\n",
    "\n",
    "        ax.vlines(q1-3*iqr, position-0.2,position+0.2, linestyle=\"dashed\", linewidth=1)\n",
    "        ax.vlines(q3+3*iqr, position-0.2,position+0.2, linestyle=\"dashed\", linewidth=1)\n",
    "\n",
    "    #  \n",
    "    plt.figtext(1,textloc,\n",
    "                r\"$\\min={:.4}$\".format(minim)+\"\\n\"+\n",
    "                r\"$q_1={:.4}$\".format(q1)+\"\\n\"+\n",
    "                r\"med$={:.4}$\".format(q2)+\"\\n\"+\n",
    "                r\"$q_3={:.4}$\".format(q3)+\"\\n\"+\n",
    "                r\"max$={:.4}$\".format(maxim),\n",
    "                ha=\"left\", va=\"top\",\n",
    "                backgroundcolor=(0.1, 0.1, 1, 0.15),\n",
    "                fontsize=\"large\")\n",
    "    \n",
    "def disp_data(ax, data):\n",
    "    ax.scatter(data, np.zeros(data.shape), zorder=2, s=10)\n",
    "    ax.set_yticks([])\n",
    "#     ax.set_xticks([])\n",
    "    mean = np.mean(data)\n",
    "    ax.scatter(mean, 0, zorder=2, s=20, color=\"red\")\n",
    "    ax.set_ylim(-0.01,0.1)\n",
    "    ax.axhline(y=0, color='k', zorder=1, linewidth=0.5)\n",
    "\n",
    "    \n",
    "    ax.spines['top'].set_visible(False)\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['left'].set_visible(False)\n",
    "    ax.spines['bottom'].set_visible(False)\n",
    "\n",
    "    ax.set_ylim(-0.1,1.5)\n",
    "            \n",
    "box_plot(ax, data2, width=0.7, showout=False, position = np.array([1]),\n",
    "         textloc = np.array([0.4]), label = \"Regular carrots\")\n",
    "\n",
    "box_plot(ax, data1, width=0.7, showout=False, position = np.array([2]),\n",
    "         textloc = np.array([0.8]), label = \"Baby carrots\" )\n",
    "\n",
    "ax.set_yticklabels([\"Regular-sized carrots\", \"Baby-sized carrots\" ])\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "array([ 1.00,  1.03,  1.05,  1.07,  1.09,  1.10,  1.10,  1.10,  1.10,  1.10,  1.11,\n",
      "        1.12,  1.13,  1.13,  1.13,  1.14,  1.14,  1.15,  1.15,  1.16,  1.16,  1.18,\n",
      "        1.18,  1.19,  1.19,  1.19,  1.19,  1.19,  1.19,  1.20,  1.20,  1.20,  1.20,\n",
      "        1.20,  1.20,  1.20,  1.20,  1.21,  1.21,  1.21,  1.21,  1.22,  1.22,  1.23,\n",
      "        1.23,  1.23,  1.23,  1.23,  1.24,  1.24,  1.24,  1.24,  1.24,  1.24,  1.25,\n",
      "        1.25,  1.26,  1.26,  1.26,  1.26,  1.26,  1.26,  1.27,  1.28,  1.28,  1.29,\n",
      "        1.29,  1.30,  1.31,  1.32,  1.33,  1.34,  1.34,  1.36,  1.43])\n"
     ]
    }
   ],
   "source": [
    "np.set_printoptions(formatter={'float': '{: 0.2f}'.format}, linewidth=90)\n",
    "print(repr(np.sort(data2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.2-6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'25,9,5,5,5,9,6,5,15,4555,6,5,6,24,21,16,5,8,77,5,5,35,13,9,5,18,6,1019,16,21,8,13,5,9,10,10,623,8,5,10,15,7,5,5,24,911,34,12,11,17,11,16,5,15,512,6,5,5,7,6,17,20,7,88,6,10,11,6,7,5,12,11,186,21,6,5,24,7,16,21,23,1511,8,6,8,14,11,6,9,6,10'"
      ]
     },
     "execution_count": 231,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s= \"25 9 5 5 5 9 6 5 15 4555 6 5 6 24 21 16 5 8 77 5 5 35 13 9 5 18 6 1019 16 21 8 13 5 9 10 10 623 8 5 10 15 7 5 5 24 911 34 12 11 17 11 16 5 15 512 6 5 5 7 6 17 20 7 88 6 10 11 6 7 5 12 11 186 21 6 5 24 7 16 21 23 1511 8 6 8 14 11 6 9 6 10\"\n",
    "\n",
    "re.sub(\"\\s+\", \",\", s.strip())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 345,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 2250x675 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import stemgraphic \n",
    "plt.rcParams[\"figure.figsize\"] = (20, 20)\n",
    "plt.rcParams['figure.dpi'] = 300\n",
    "\n",
    "# generate data\n",
    "data = np.array([25,9,5,5,5,9,6,5,15,45, 55,6,5,6,\n",
    "                  24,21,16,5,8,7,7,5,5,35,13,9,5,18,\n",
    "                  6,10, 19,16,21,8,13,5,9,10,10,6, 23,8,\n",
    "                  5,10,15,7,5,5,24,9, 11,34,12,11,17,11,\n",
    "                  16,5,15,5, 12,6,5,5,7,6,17,20,7,8, 8,6,\n",
    "                  10,11,6,7,5,12,11,18, 6,21,6,5,24,7,16,\n",
    "                  21,23,15, 11,8,6,8,14,11,6,9,6,10])\n",
    "\n",
    "stemgraphic.stem_graphic(data, scale = 10, legend_pos=None, \n",
    "                         alpha=0,outliers=False) \n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 325,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100,)"
      ]
     },
     "execution_count": 325,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 362,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23.0"
      ]
     },
     "execution_count": 362,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sort(data)[90]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 337,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.set_printoptions()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([25,  9,  5,  5,  5,  9,  6,  5, 15, 45, 55,  6,  5,  6, 24, 21, 16,  5,  8,  7,\n",
       "        7,  5,  5, 35, 13,  9,  5, 18,  6, 10, 19, 16, 21,  8, 13,  5,  9, 10, 10,  6,\n",
       "       23,  8,  5, 10, 15,  7,  5,  5, 24,  9, 11, 34, 12, 11, 17, 11, 16,  5, 15,  5,\n",
       "       12,  6,  5,  5,  7,  6, 17, 20,  7,  8,  8,  6, 10, 11,  6,  7,  5, 12, 11, 18,\n",
       "        6, 21,  6,  5, 24,  7, 16, 21, 23, 15, 11,  8,  6,  8, 14, 11,  6,  9,  6, 10])"
      ]
     },
     "execution_count": 328,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 359,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iqr=9.0\n",
      "\n",
      "left inner fence=-7.5\n",
      "right inner fence=28.5\n",
      "left outer fence=-21.0\n",
      "right ouer fence=42.0\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 3000x1500 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# set up the figure\n",
    "fig, ax = plt.subplots(1,1, figsize=(10,5))\n",
    "\n",
    "# generate data\n",
    "# generate data\n",
    "data = np.array([25,9,5,5,5,9,6,5,15,45, 55,6,5,6,\n",
    "                  24,21,16,5,8,7,7,5,5,35,13,9,5,18,\n",
    "                  6,10, 19,16,21,8,13,5,9,10,10,6, 23,8,\n",
    "                  5,10,15,7,5,5,24,9, 11,34,12,11,17,11,\n",
    "                  16,5,15,5, 12,6,5,5,7,6,17,20,7,8, 8,6,\n",
    "                  10,11,6,7,5,12,11,18, 6,21,6,5,24,7,16,\n",
    "                  21,23,15, 11,8,6,8,14,11,6,9,6,10]).astype(float)\n",
    "\n",
    "\n",
    "\n",
    "def percentile(data, p):\n",
    "    \"\"\"\n",
    "    Compute the percentiles the way we defined in class \n",
    "    data : array of size N \n",
    "    p : percentile\n",
    "    \"\"\"\n",
    "    data = np.sort(data, axis=0)\n",
    "    rank = int(p * (data.shape[0] + 1) - 1) # the rank\n",
    "    assert rank > 0, \"the rank does not exist\" \n",
    "    alpha = p * (data.shape[0] + 1) - 1 - rank # the fractional part\n",
    "    return data[rank] + alpha * (data[rank + 1] - data [rank])\n",
    "\n",
    "def box_plot(ax, data, width=0.4, showout = True, position = np.array([0.4]), \n",
    "             textloc=np.array([0.8]), label = \"\"):\n",
    "    \"\"\"\n",
    "    ax : matplotlib ax\n",
    "    data : the data \n",
    "    width : box width\n",
    "    showout : show the outliers   \n",
    "    position: the y axis of the box plot\n",
    "    \"\"\"\n",
    "    # compute the five number summary \n",
    "    minim = np.min(data)\n",
    "    maxim = np.max(data)\n",
    "    q1 = percentile(data, 0.25)\n",
    "    q2 = np.median(data)\n",
    "    q3 = percentile(data, 0.75)\n",
    "\n",
    "    # interquartile range\n",
    "    iqr = q3 - q1\n",
    "\n",
    "    # inner fences\n",
    "    left_innerfence = q1 - 1.5 * iqr\n",
    "    right_innerfence = q3 + 1.5 * iqr\n",
    "\n",
    "    # compute outliers \n",
    "    outliers = []\n",
    "    \n",
    "    # whiskers\n",
    "    if showout==True:\n",
    "        outliers = data[np.logical_or(data <left_innerfence, data >= right_innerfence)]\n",
    "        low_whisker = np.min(data[data >= left_innerfence])\n",
    "        high_whisker = np.max(data[data <= right_innerfence])\n",
    "    else:\n",
    "        low_whisker = np.min(data)\n",
    "        high_whisker = np.max(data)\n",
    "\n",
    "\n",
    "\n",
    "    stats = [{'iqr': iqr,\n",
    "              'whishi': high_whisker,\n",
    "              'whislo': low_whisker,\n",
    "              'fliers': outliers,\n",
    "              'q1': q1,\n",
    "              'med': q2,\n",
    "              'q3': q3}]\n",
    "\n",
    "    # add the box plot\n",
    "    flierprops = dict(markerfacecolor='black', markersize=5)\n",
    "    ax.bxp(stats, vert = False, widths=width, positions = position, \n",
    "           flierprops=flierprops, showfliers=showout)\n",
    "\n",
    "    # add Tukey's fences\n",
    "    if showout==True:\n",
    "        ax.vlines(q1-1.5*iqr, position-0.2,position+0.2, linestyle=\"dashed\", linewidth=1)\n",
    "        ax.vlines(q3+1.5*iqr, position-0.2,position+0.2, linestyle=\"dashed\", linewidth=1)\n",
    "\n",
    "        ax.vlines(q1-3*iqr, position-0.2,position+0.2, linestyle=\"dashed\", linewidth=1)\n",
    "        ax.vlines(q3+3*iqr, position-0.2,position+0.2, linestyle=\"dashed\", linewidth=1)\n",
    "    print (\"iqr={}\\n\".format(iqr)+\"\\n\"+\n",
    "           \"left inner fence={}\".format(q1-1.5*iqr)+\"\\n\"+\n",
    "           \"right inner fence={}\".format(q3+1.5*iqr)+\"\\n\"+\n",
    "           \"left outer fence={}\".format(q1-3*iqr)+\"\\n\"+\n",
    "           \"right ouer fence={}\".format(q3+3*iqr)\n",
    "          )\n",
    "    #  \n",
    "    ax.set_yticks([])\n",
    "    plt.figtext(1,textloc,\n",
    "                r\"$\\min={:.4}$\".format(minim)+\"\\n\"+\n",
    "                r\"$q_1={:.4}$\".format(q1)+\"\\n\"+\n",
    "                r\"med$={:.4}$\".format(q2)+\"\\n\"+\n",
    "                r\"$q_3={:.4}$\".format(q3)+\"\\n\"+\n",
    "                r\"max$={:.4}$\".format(maxim),\n",
    "                ha=\"left\", va=\"top\",\n",
    "                backgroundcolor=(0.1, 0.1, 1, 0.15),\n",
    "                fontsize=\"large\")\n",
    "    \n",
    "def disp_data(ax, data):\n",
    "    ax.scatter(data, np.zeros(data.shape), zorder=2, s=10)\n",
    "    ax.set_yticks([])\n",
    "#     ax.set_xticks([])\n",
    "    mean = np.mean(data)\n",
    "    ax.scatter(mean, 0, zorder=2, s=20, color=\"red\")\n",
    "    ax.set_ylim(-0.01,0.1)\n",
    "    ax.axhline(y=0, color='k', zorder=1, linewidth=0.5)\n",
    "\n",
    "    \n",
    "    ax.spines['top'].set_visible(False)\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['left'].set_visible(False)\n",
    "    ax.spines['bottom'].set_visible(False)\n",
    "\n",
    "    ax.set_ylim(-0.1,1.5)\n",
    "            \n",
    "\n",
    "box_plot(ax, data, width=0.7, showout=True, position = np.array([1]),\n",
    "         textloc = np.array([0.8])  )\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 363,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.8"
      ]
     },
     "execution_count": 363,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "21+0.9* (23-21)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 364,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.80000000000001"
      ]
     },
     "execution_count": 364,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "percentile(data, 0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.4-6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 369,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'31.5+36.9+33.8+30.1+33.9+35.2+29.6+34.4+30.5+34.2+31.6+36.7+35.8+34.5+32.7'"
      ]
     },
     "execution_count": 369,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s=\"31.5 36.9 33.8 30.1 33.9 35.2 29.6 34.4 30.5 34.2 31.6 36.7 35.8 34.5 32.7\"\n",
    "\n",
    "re.sub(\"\\s+\", \",\", s.strip())\n",
    "\n",
    "re.sub(\"\\s+\", \"+\", s.strip())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 368,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean = 33.42666666666666\n",
      "var = 5.097955555555554\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "data = np.array([31.5,36.9,33.8,30.1,33.9,35.2,29.6,34.4,30.5,34.2,31.6,36.7,35.8,34.5,32.7])\n",
    "\n",
    "print(\"mean = {}\".format(np.mean(data))+\"\\n\"+\"var = {}\".format(np.var(data)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.1-7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 371,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'21.50,18.95,18.55,19.40,19.15,22.35,22.90,22.20,23.10'"
      ]
     },
     "execution_count": 371,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s=\"21.50 18.95 18.55 19.40 19.15 22.35 22.90 22.20 23.10\"\n",
    "\n",
    "re.sub(\"\\s+\", \",\", s.strip())\n",
    "\n",
    "# re.sub(\"\\s+\", \"+\", s.strip())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 375,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean = 20.9\n",
      "S = 1.8584267540045805\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "data = np.array([21.50,18.95,18.55,19.40,19.15,22.35,22.90,22.20,23.10])\n",
    "\n",
    "print(\"mean = {}\".format(np.mean(data))+\"\\n\"+\"S = {}\".format(np.sqrt(np.var(data, ddof=1))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.1-5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'93,140,8,120,3,120,33,70,91,61,7,100,19,98,110,23,14,94,57,9,66,53,28,76,58,9,73,49,37,92'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import re\n",
    "\n",
    "s=\"93 140 8 120 3 120 33 70 91 61 7 100 19 98 110 23 14 94 57 9 66 53 28 76 58 9 73 49 37 92\"\n",
    "\n",
    "re.sub(\"\\s+\", \",\", s.strip())\n",
    "\n",
    "# re.sub(\"\\s+\", \"+\", s.strip())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "46.42 6.456159849322196\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "data=np.array([37.4, 48.8, 46.9, 55.0, 44.0])\n",
    "\n",
    "print(np.mean(data), np.sqrt(np.var(data, ddof=1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.1-8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "60.36666666666667 39.621905586415835\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "data=np.array([93,140,8,120,3,120,33,70,91,61,7,100,19,98,110,23,14,94,57,9,66,53,28,76,58,9,73,49,37,92])\n",
    "\n",
    "print(np.mean(data), np.sqrt(np.var(data, ddof=1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.1-8 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'3.4,3.6,3.8,3.3,3.4,3.5,3.7,3.6,3.7'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import re\n",
    "\n",
    "s=\"3.4 3.6 3.8 3.3 3.4 3.5 3.7 3.6 3.7\"\n",
    "\n",
    "re.sub(\"\\s+\", \",\", s.strip())\n",
    "\n",
    "# re.sub(\"\\s+\", \"+\", s.strip())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.5555555555555554 0.1666666666666667\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "data=np.array([3.4,3.6,3.8,3.3,3.4,3.5,3.7,3.6,3.7])\n",
    "\n",
    "print(np.mean(data), np.sqrt(np.var(data, ddof=1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.1-12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "265,272,246,260,274,263,255,258,276,274,274,269,244,212,235,254,224\n",
      "252,276,243,246,275,246,244,245,259,260,267,267,251,222,235,255,231\n"
     ]
    }
   ],
   "source": [
    "import re\n",
    "\n",
    "s1=\"265 272 246 260 274 263 255 258 276 274 274 269 244 212 235 254 224\"\n",
    "s2=\"252 276 243 246 275 246 244 245 259 260 267 267 251 222 235 255 231\"\n",
    "\n",
    "print(re.sub(\"\\s+\", \",\", s1.strip()))\n",
    "print(re.sub(\"\\s+\", \",\", s2.strip()))\n",
    "\n",
    "# re.sub(\"\\s+\", \"+\", s.strip())\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.764705882352941 9.086593226869367\n"
     ]
    }
   ],
   "source": [
    "D1=np.array([265,272,246,260,274,263,255,258,276,274,274,269,244,212,235,254,224])\n",
    "D2=np.array([252,276,243,246,275,246,244,245,259,260,267,267,251,222,235,255,231])\n",
    "data=D1-D2\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "print(np.mean(data), np.sqrt(np.var(data, ddof=1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Final\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# set up the figure\n",
    "fig, ax = plt.subplots(1,1, figsize=(12,5))\n",
    "\n",
    "# data\n",
    "data = np.array([0.1, 0.5, 1, 1.2, 3, 0.8, 1.6, -3, 2, 10]).astype(float)\n",
    "# data = np.array([-30,-1, -5, -0.5, 0.5, 0.6, 0, 2, 3, 4.6, 4, 7, 18, 35]).astype(float)\n",
    "\n",
    "\n",
    "def percentile(data, p):\n",
    "    \"\"\"\n",
    "    Compute the percentiles the way we defined in class \n",
    "    data : array of size N \n",
    "    p : percentile\n",
    "    \"\"\"\n",
    "    data = np.sort(data, axis=0)\n",
    "    rank = int(p * (data.shape[0] + 1) - 1) # the rank\n",
    "    assert rank > 0, \"the rank does not exist\" \n",
    "    alpha = p * (data.shape[0] + 1) - 1 - rank # the fractional part\n",
    "    return data[rank] + alpha * (data[rank + 1] - data [rank])\n",
    "\n",
    "def box_plot(ax, data, width=0.4, showout = True, position = np.array([0.4])):\n",
    "    \"\"\"\n",
    "    ax : matplotlib ax\n",
    "    data : the data \n",
    "    width : box width\n",
    "    showout : show the outliers   \n",
    "    position: the y axis of the box plot\n",
    "    \"\"\"\n",
    "    # compute the five number summary \n",
    "    minim = np.min(data)\n",
    "    maxim = np.max(data)\n",
    "    q1 = percentile(data, 0.25)\n",
    "    q2 = np.median(data)\n",
    "    q3 = percentile(data, 0.75)\n",
    "\n",
    "    # interquartile range\n",
    "    iqr = q3 - q1\n",
    "\n",
    "    # inner fences\n",
    "    left_innerfence = q1 - 1.5 * iqr\n",
    "    right_innerfence = q3 + 1.5 * iqr\n",
    "\n",
    "    # compute outliers \n",
    "    outliers = data[np.logical_or(data <left_innerfence, data >= right_innerfence)]\n",
    "    \n",
    "    # whiskers\n",
    "    if showout==True:\n",
    "        low_whisker = np.min(data[data >= left_innerfence])\n",
    "        high_whisker = np.max(data[data <= right_innerfence])\n",
    "    else:\n",
    "        low_whisker = np.min(data)\n",
    "        high_whisker = np.max(data)\n",
    "\n",
    "\n",
    "\n",
    "    stats = [{'iqr': iqr,\n",
    "              'whishi': high_whisker,\n",
    "              'whislo': low_whisker,\n",
    "              'fliers': outliers,\n",
    "              'q1': q1,\n",
    "              'med': q2,\n",
    "              'q3': q3}]\n",
    "\n",
    "    # add the box plot\n",
    "    flierprops = dict(markerfacecolor='black', markersize=5)\n",
    "    ax.bxp(stats, vert = False, widths=width, positions = position, \n",
    "           flierprops=flierprops, showfliers=showout)\n",
    "\n",
    "    # add Tukey's fences\n",
    "    if showout==True:\n",
    "        ax.vlines(q1-1.5*iqr, position-0.2,position+0.2, linestyle=\"dashed\", linewidth=1)\n",
    "        ax.vlines(q3+1.5*iqr, position-0.2,position+0.2, linestyle=\"dashed\", linewidth=1)\n",
    "\n",
    "        ax.vlines(q1-3*iqr, position-0.2,position+0.2, linestyle=\"dashed\", linewidth=1)\n",
    "        ax.vlines(q3+3*iqr, position-0.2,position+0.2, linestyle=\"dashed\", linewidth=1)\n",
    "\n",
    "    #  \n",
    "    ax.spines['top'].set_visible(False)\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['left'].set_visible(False)\n",
    "    ax.set_ylim(-0.1,position+0.3)\n",
    "    ax.set_yticks([])\n",
    "    plt.figtext(1,0.8,\n",
    "                r\"$\\min={:.4}$\".format(minim)+\"\\n\"+\n",
    "                r\"$q_1={:.4}$\".format(q1)+\"\\n\"+\n",
    "                r\"med$={:.4}$\".format(q2)+\"\\n\"+\n",
    "                r\"$q_3={:.4}$\".format(q3)+\"\\n\"+\n",
    "                r\"max$={:.4}$\".format(maxim),\n",
    "                ha=\"left\", va=\"top\",\n",
    "                backgroundcolor=(0.1, 0.1, 1, 0.15),\n",
    "                fontsize=\"large\")\n",
    "    \n",
    "def disp_data(ax, data):\n",
    "    ax.scatter(data, np.zeros(data.shape), zorder=2, s=10)\n",
    "    ax.set_yticks([])\n",
    "#     ax.set_xticks([])\n",
    "    mean = np.mean(data)\n",
    "    ax.scatter(mean, 0, zorder=2, s=20, color=\"red\")\n",
    "    ax.set_ylim(-0.01,0.1)\n",
    "    ax.axhline(y=0, color='k', zorder=1, linewidth=0.5)\n",
    "\n",
    "    \n",
    "    ax.spines['top'].set_visible(False)\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['left'].set_visible(False)\n",
    "    ax.spines['bottom'].set_visible(False)\n",
    "\n",
    "    ax.set_ylim(-0.1,1.5)\n",
    "            \n",
    "box_plot(ax, data, width=0.2, showout=True)\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## problem 4\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "plt.figure(figsize=(15,10)) \n",
    "\n",
    "meanx=1\n",
    "meany=2\n",
    "varx=1/3\n",
    "cov = 6/5\n",
    "\n",
    "def pdf(X,Y):\n",
    "    Z = np.zeros(X.shape)    \n",
    "    cond = (0<=X) & (X<=4) & (-1/2<=Y-X**3) & (Y-X**3<=1/2)\n",
    "    Z[cond] = 1/4\n",
    "    return Z\n",
    "\n",
    "x = np.linspace(0, 2, 1000)\n",
    "y = np.linspace(-2, 8.5 , 1000)\n",
    "\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z = pdf(X, Y)\n",
    "\n",
    "plt.contourf(X, Y, Z, 20,  cmap = \"Blues\", zorder=1)\n",
    "cb=plt.colorbar()\n",
    "cb.remove()\n",
    "\n",
    "xval = np.linspace(0, 2, 100)\n",
    "plt.plot(xval,xval**3, linewidth=4, label=\"conditional mean function\", color=(0.2,0.7,0.3), zorder=2)\n",
    "yval = (xval-meanx)*cov/varx + meany\n",
    "plt.plot(xval,yval,   linewidth=4, label=\"least squares line\", color=\"y\", zorder=3)\n",
    "plt.scatter(meanx, meany, color = \"red\", s=200 , label =\"mean\", zorder=4)  \n",
    "\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "# plt.title(\"Fitting least squares line and conditional mean to a joint distribution\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.draw()\n",
    "\n",
    "\n",
    "        \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### problem 5\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iqr=1.85\n",
      "\n",
      "left inner fence=-2.3750000000000004\n",
      "right inner fence=5.025\n",
      "left outer fence=-5.15\n",
      "right ouer fence=7.800000000000001\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# nbi:hide_in\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# set up the figure\n",
    "fig, ax = plt.subplots(1,1, figsize=(10,5))\n",
    "\n",
    "# generate data\n",
    "# generate data\n",
    "data = np.array([0.1, 0.5, 1, 1.2, 3, 0.8, 1.6, -3, 2, 10]).astype(float)\n",
    "\n",
    "\n",
    "\n",
    "def percentile(data, p):\n",
    "    \"\"\"\n",
    "    Compute the percentiles the way we defined in class \n",
    "    data : array of size N \n",
    "    p : percentile\n",
    "    \"\"\"\n",
    "    data = np.sort(data, axis=0)\n",
    "    rank = int(p * (data.shape[0] + 1) - 1) # the rank\n",
    "    assert rank > 0, \"the rank does not exist\" \n",
    "    alpha = p * (data.shape[0] + 1) - 1 - rank # the fractional part\n",
    "    return data[rank] + alpha * (data[rank + 1] - data [rank])\n",
    "\n",
    "def box_plot(ax, data, width=0.4, showout = True, position = np.array([0.4]), \n",
    "             textloc=np.array([0.8]), label = \"\"):\n",
    "    \"\"\"\n",
    "    ax : matplotlib ax\n",
    "    data : the data \n",
    "    width : box width\n",
    "    showout : show the outliers   \n",
    "    position: the y axis of the box plot\n",
    "    \"\"\"\n",
    "    # compute the five number summary \n",
    "    minim = np.min(data)\n",
    "    maxim = np.max(data)\n",
    "    q1 = percentile(data, 0.25)\n",
    "    q2 = np.median(data)\n",
    "    q3 = percentile(data, 0.75)\n",
    "\n",
    "    # interquartile range\n",
    "    iqr = q3 - q1\n",
    "\n",
    "    # inner fences\n",
    "    left_innerfence = q1 - 1.5 * iqr\n",
    "    right_innerfence = q3 + 1.5 * iqr\n",
    "\n",
    "    # compute outliers \n",
    "    outliers = []\n",
    "    \n",
    "    # whiskers\n",
    "    if showout==True:\n",
    "        outliers = data[np.logical_or(data <left_innerfence, data >= right_innerfence)]\n",
    "        low_whisker = np.min(data[data >= left_innerfence])\n",
    "        high_whisker = np.max(data[data <= right_innerfence])\n",
    "    else:\n",
    "        low_whisker = np.min(data)\n",
    "        high_whisker = np.max(data)\n",
    "\n",
    "\n",
    "\n",
    "    stats = [{'iqr': iqr,\n",
    "              'whishi': high_whisker,\n",
    "              'whislo': low_whisker,\n",
    "              'fliers': outliers,\n",
    "              'q1': q1,\n",
    "              'med': q2,\n",
    "              'q3': q3}]\n",
    "\n",
    "    # add the box plot\n",
    "    flierprops = dict(markerfacecolor='black', markersize=5)\n",
    "    ax.bxp(stats, vert = False, widths=width, positions = position, \n",
    "           flierprops=flierprops, showfliers=showout)\n",
    "\n",
    "    # add Tukey's fences\n",
    "    if showout==True:\n",
    "        ax.vlines(q1-1.5*iqr, position-0.2,position+0.2, linestyle=\"dashed\", linewidth=1)\n",
    "        ax.vlines(q3+1.5*iqr, position-0.2,position+0.2, linestyle=\"dashed\", linewidth=1)\n",
    "\n",
    "        ax.vlines(q1-3*iqr, position-0.2,position+0.2, linestyle=\"dashed\", linewidth=1)\n",
    "        ax.vlines(q3+3*iqr, position-0.2,position+0.2, linestyle=\"dashed\", linewidth=1)\n",
    "    print (\"iqr={}\\n\".format(iqr)+\"\\n\"+\n",
    "           \"left inner fence={}\".format(q1-1.5*iqr)+\"\\n\"+\n",
    "           \"right inner fence={}\".format(q3+1.5*iqr)+\"\\n\"+\n",
    "           \"left outer fence={}\".format(q1-3*iqr)+\"\\n\"+\n",
    "           \"right ouer fence={}\".format(q3+3*iqr)\n",
    "          )\n",
    "    #  \n",
    "    ax.set_yticks([])\n",
    "    plt.figtext(1,textloc,\n",
    "                r\"$\\min={:.4}$\".format(minim)+\"\\n\"+\n",
    "                r\"$q_1={:.4}$\".format(q1)+\"\\n\"+\n",
    "                r\"med$={:.4}$\".format(q2)+\"\\n\"+\n",
    "                r\"$q_3={:.4}$\".format(q3)+\"\\n\"+\n",
    "                r\"max$={:.4}$\".format(maxim),\n",
    "                ha=\"left\", va=\"top\",\n",
    "                backgroundcolor=(0.1, 0.1, 1, 0.15),\n",
    "                fontsize=\"large\")\n",
    "    \n",
    "def disp_data(ax, data):\n",
    "    ax.scatter(data, np.zeros(data.shape), zorder=2, s=10)\n",
    "    ax.set_yticks([])\n",
    "#     ax.set_xticks([])\n",
    "    mean = np.mean(data)\n",
    "    ax.scatter(mean, 0, zorder=2, s=20, color=\"red\")\n",
    "    ax.set_ylim(-0.01,0.1)\n",
    "    ax.axhline(y=0, color='k', zorder=1, linewidth=0.5)\n",
    "\n",
    "    \n",
    "    ax.spines['top'].set_visible(False)\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['left'].set_visible(False)\n",
    "    ax.spines['bottom'].set_visible(False)\n",
    "\n",
    "    ax.set_ylim(-0.1,1.5)\n",
    "            \n",
    "\n",
    "box_plot(ax, data, width=0.7, showout=True, position = np.array([1]),\n",
    "         textloc = np.array([0.8])  )\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3. ,  0.1,  0.5,  0.8,  1. ,  1.2,  1.6,  2. ,  3. , 10. ])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sort(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "data=np.array([423.90,   420.24,   431.00,   418.76,   \n",
    "               428.68,   423.64,   430.65,   432.92,  \n",
    "               421.93,   433.97,   426.10,   430.20])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "426.8325"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.105124208265479"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(np.var(data, ddof=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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",
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