Section 5 is done

section_4/.ipynb_checkpoints/22_plotting_images-checkpoint.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "df = pd.read_csv(\"train.csv\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(42000, 785)"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "C:\\Users\\litak\\Anaconda3\\envs\\tensorflow-cpu\\lib\\site-packages\\ipykernel_launcher.py:1: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
+      "  \"\"\"Entry point for launching an IPython kernel.\n"
+     ]
+    }
+   ],
+   "source": [
+    "M = df.as_matrix()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(784,)"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "im = M[0,1:]\n",
+    "im.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(28, 28)"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "im = im.reshape(28, 28)\n",
+    "im.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.imshow(im)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "M[0,0]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.imshow(im, cmap='gray')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.imshow(255 - im, cmap='gray')\n",
+    "plt.show()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

section_4/22_plotting_images.ipynb

@@ -182,13 +182,6 @@
     "plt.imshow(255 - im, cmap='gray')\n",
     "plt.imshow(255 - im, cmap='gray')\n",
     "plt.show()"
     "plt.show()"
    ]
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
   }
  ],
  ],
  "metadata": {
  "metadata": {

section_5/23_gaussian_pdf_and_cdf.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from scipy.stats import norm\n",
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.3989422804014327"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "norm.pdf(0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.03520653267642995"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "norm.pdf(0, loc=5, scale=10)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([0.34427719, 0.38355058, 0.37368751, 0.37774103, 0.28487339,\n",
+       "       0.38220885, 0.23882119, 0.36822956, 0.39686933, 0.38577969])"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "r = np.random.randn(10)\n",
+    "norm.pdf(r)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([-1.06630816, -0.95828377, -0.98433536, -0.97354641, -1.25571044,\n",
+       "       -0.96178809, -1.43204019, -0.99904872, -0.9241482 , -0.95248884])"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "norm.logpdf(r)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([0.7064003 , 0.38953997, 0.64119472, 0.37051938, 0.7940906 ,\n",
+       "       0.38485887, 0.15552604, 0.65552315, 0.45934851, 0.39780302])"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "norm.cdf(r)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([-0.3475732 , -0.94278879, -0.4444221 , -0.99284953, -0.23055771,\n",
+       "       -0.95487857, -1.86094212, -0.42232166, -0.77794609, -0.92179832])"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "norm.logcdf(r)"
+   ]
+  },
+  {
+   "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",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

section_5/24_sampling_from_gaussian_distribution.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from scipy.stats import norm\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "r = np.random.randn(10000)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD8CAYAAAB5Pm/hAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAEN9JREFUeJzt3X+M5HV9x/Hnq5SiUVukHHjejx6x10Y0erQbSsM/FKzBH/G0KRbS4tVePP+AqIlJBUyKTUuCsUpp2tKchQgtikQlXJAWETXExB8cSBE4ba96lc1duFNBMabYO979Y7+r4zF3O7szczP72ecj2ezMZz6z887dzmvf+/l+vt9NVSFJatcvTLoASdJ4GfSS1DiDXpIaZ9BLUuMMeklqnEEvSY0z6CWpcQa9JDXOoJekxv3ipAsAOPnkk2vDhg2TLkOSlpX777//u1W1aqF5UxH0GzZsYOfOnZMuQ5KWlST/M8g8l24kqXEGvSQ1zqCXpMYZ9JLUOINekhpn0EtS4wx6SWqcQS9JjTPoJalxU3FmrDROGy779E9v77n6dROsRJoMO3pJapxBL0mNM+glqXGu0UtL5Nq/lgs7eklq3IIdfZLnAPcCJ3TzP1FVVyY5DbgFOAl4ALi4qn6S5ATgJuC3ge8Bf1RVe8ZUvzQWdutqySAd/dPAuVX1SmATcH6Ss4D3A9dU1UbgCWBrN38r8ERV/TpwTTdPkjQhCwZ9zflRd/f47qOAc4FPdOM3Am/sbm/u7tM9fl6SjKxiSdKiDLRGn+S4JA8C+4G7gf8Gnqyqg92UWWBNd3sN8BhA9/gPgF8dZdGSpMENtOumqg4Bm5KcCNwGvLTftO5zv+69Dh9Isg3YBrB+/fqBipUmrXftXlouFrXrpqqeBL4AnAWcmGT+B8VaYG93exZYB9A9/ivA9/t8re1VNVNVM6tWLfhHzCVJSzTIrptVwP9V1ZNJngu8irkDrJ8H/pC5nTdbgNu7p+zo7n+pe/xzVfWsjl4aJztv6WcGWbpZDdyY5DjmfgO4taruSPIocEuSvwa+Blzfzb8e+Jcku5nr5C8cQ93S0A7/YeA2SrVqwaCvqoeAM/qMfws4s8/4/wIXjKQ6SdLQPDNWkhpn0EtS47yomZY1L1UgLcyOXpIaZ9BLUuMMeklqnEEvSY0z6CWpcQa9JDXOoJekxrmPXlqAF0jTcmdHL0mNs6PXsnAszoC1c1erDHpNFS9pII2eSzeS1DiDXpIaZ9BLUuMMeklqnEEvSY0z6CWpcQa9JDXOffRadjyxSVocg14T4YlR0rHj0o0kNW7Bjj7JOuAm4EXAM8D2qro2yfuAtwEHuqlXVNWd3XMuB7YCh4B3VNVdY6hdWjSXfbQSDbJ0cxB4d1U9kOQFwP1J7u4eu6aq/qZ3cpLTgQuBlwEvBj6b5Deq6tAoC1f7DGVpNBYM+qraB+zrbj+VZBew5ihP2QzcUlVPA99Oshs4E/jSCOqVppLHHDTNFrVGn2QDcAbwlW7o0iQPJbkhyQu7sTXAYz1Pm6XPD4Yk25LsTLLzwIEDhz8sSRqRgYM+yfOBTwLvqqofAtcBLwE2Mdfxf3B+ap+n17MGqrZX1UxVzaxatWrRhUuSBjPQ9sokxzMX8jdX1acAqurxnsc/DNzR3Z0F1vU8fS2wdyTVqkmjWot3TV/qb8GOPkmA64FdVfWhnvHVPdPeBDzc3d4BXJjkhCSnARuBr46uZEnSYgzS0Z8NXAx8PcmD3dgVwEVJNjG3LLMHeDtAVT2S5FbgUeZ27FzijhtJmpxBdt18kf7r7nce5TlXAVcNUZe0bLkDR9PGM2MlqXFe60Y6Ruz0NSl29JLUODt6HTNuf5Qmw45ekhpn0EtS4wx6SWqcQS9JjfNgrDRGHoDWNLCjl6TGGfSS1DiDXpIaZ9BLUuMMeklqnEEvSY0z6CWpce6jlybASxbrWLKjl6TGGfSS1DiDXpIaZ9BLUuMMeklqnEEvSY0z6CWpcQvuo0+yDrgJeBHwDLC9qq5NchLwcWADsAd4c1U9kSTAtcBrgR8Df1pVD4ynfE0j94hL02WQjv4g8O6qeilwFnBJktOBy4B7qmojcE93H+A1wMbuYxtw3cirliQNbMGgr6p98x15VT0F7ALWAJuBG7tpNwJv7G5vBm6qOV8GTkyyeuSVS5IGsqg1+iQbgDOArwCnVtU+mPthAJzSTVsDPNbztNlu7PCvtS3JziQ7Dxw4sPjKJUkDGfhaN0meD3wSeFdV/XBuKb7/1D5j9ayBqu3AdoCZmZlnPa42+DdTpckbqKNPcjxzIX9zVX2qG358fkmm+7y/G58F1vU8fS2wdzTlSpIWa8Gg73bRXA/sqqoP9Ty0A9jS3d4C3N4z/pbMOQv4wfwSjyTp2Btk6eZs4GLg60ke7MauAK4Gbk2yFfgOcEH32J3Mba3czdz2yreOtGJJ0qIsGPRV9UX6r7sDnNdnfgGXDFmXJGlEPDNWkhpn0EtS4wx6SWqcQS9JjTPoJalxA58ZK2n8vPKnxsGOXpIaZ0cvTdiRrgdkd69RsaOXpMYZ9JLUOINekhpn0EtS4wx6SWqcQS9JjXN7pUbCPxkoTS87eklqnEEvSY0z6CWpcQa9JDXOoJekxhn0ktQ4t1dqydxSKS0PdvSS1DiDXpIat+DSTZIbgNcD+6vq5d3Y+4C3AQe6aVdU1Z3dY5cDW4FDwDuq6q4x1C2tKEdaJvMPkmgQg3T0HwHO7zN+TVVt6j7mQ/504ELgZd1z/jHJcaMqVpK0eAsGfVXdC3x/wK+3Gbilqp6uqm8Du4Ezh6hPkjSkYdboL03yUJIbkrywG1sDPNYzZ7Ybe5Yk25LsTLLzwIED/aZIkkZgqUF/HfASYBOwD/hgN54+c6vfF6iq7VU1U1Uzq1atWmIZkqSFLCnoq+rxqjpUVc8AH+ZnyzOzwLqeqWuBvcOVKEkaxpKCPsnqnrtvAh7ubu8ALkxyQpLTgI3AV4crUZI0jEG2V34MOAc4OckscCVwTpJNzC3L7AHeDlBVjyS5FXgUOAhcUlWHxlO6JGkQCwZ9VV3UZ/j6o8y/CrhqmKIkSaPjmbGS1DiDXpIaZ9BLUuO8TLEWxUsTS8uPHb0kNc6OXguyi5eWNzt6SWqcQS9JjTPoJalxBr0kNc6gl6TGGfSS1Di3V6ovt1RK7TDopUb0/nDec/XrJliJpo1LN5LUOINekhpn0EtS41yjlxrker162dFLUuPs6KVlzG2wGoQdvSQ1zqCXpMYZ9JLUuAWDPskNSfYnebhn7KQkdyf5r+7zC7vxJPm7JLuTPJTkt8ZZvCRpYYN09B8Bzj9s7DLgnqraCNzT3Qd4DbCx+9gGXDeaMiVJS7Vg0FfVvcD3DxveDNzY3b4ReGPP+E0158vAiUlWj6pYSdLiLXWN/tSq2gfQfT6lG18DPNYzb7YbkyRNyKj30afPWPWdmGxjbnmH9evXj7gMLYV7stvkWbJaakf/+PySTPd5fzc+C6zrmbcW2NvvC1TV9qqaqaqZVatWLbEMSdJClhr0O4At3e0twO0942/pdt+cBfxgfolHkjQZCy7dJPkYcA5wcpJZ4ErgauDWJFuB7wAXdNPvBF4L7AZ+DLx1DDVLkhZhwaCvqouO8NB5feYWcMmwRUmSRseLmkkriAdmVyYvgSBJjTPoJalxBr0kNc41+hXIdVppZbGjl6TGGfSS1DiDXpIaZ9BLUuMMeklqnLtuVjgvTbxyuftq5bCjl6TGGfSS1DiDXpIaZ9BLUuM8GCvJA7ONs6OXpMYZ9JLUOINekhrnGv0K4ElR0spm0DfEA2oahcMbA7+Xlj+XbiSpcQa9JDXOoJekxg21Rp9kD/AUcAg4WFUzSU4CPg5sAPYAb66qJ4YrU4vlAVhJ80bR0f9eVW2qqpnu/mXAPVW1Ebinuy9JmpBx7LrZDJzT3b4R+ALwnjG8jqRjwN1cy9+wHX0Bn0lyf5Jt3dipVbUPoPt8ypCvIUkawrAd/dlVtTfJKcDdSb4x6BO7HwzbANavXz9kGZKkIxkq6Ktqb/d5f5LbgDOBx5Osrqp9SVYD+4/w3O3AdoCZmZkapo6VxgOtkhZjyUs3SZ6X5AXzt4FXAw8DO4At3bQtwO3DFilJWrphOvpTgduSzH+dj1bVvye5D7g1yVbgO8AFw5cpu3hNAw/MLk9LDvqq+hbwyj7j3wPOG6YoSdPP0F8+PDNWkhpn0EtS4wx6SWqc16OXNDTX66ebHb0kNc6gl6TGGfSS1DiDXpIa58HYKebZsJJGwaCfAga6pHFy6UaSGmdHL2mk3FM/fezoJalxdvQT4rq8Vho7/cmxo5ekxtnRH0N28ZImwY5ekhqXqsn/Xe6ZmZnauXPnpMsYC7t46ehcr1+6JPdX1cxC8+zoJalxBr0kNc6gl6TGuetmCO4LloZ3pPfRkY5v+V5bPIN+DDwAKy2N753xMOhHxG9QSdNqbEGf5HzgWuA44J+r6upxvda4uUQjTQ/fj4s3lqBPchzwD8DvA7PAfUl2VNWj43i9UfEbSFpexrGO32IOjKujPxPYXVXfAkhyC7AZGHnQH+0/ZbEHeY703EHGJU2PQX4ATPK9fKx/mIwr6NcAj/XcnwV+Z0yv9VNH+48zoCUda9Py28G4gj59xn7uWgtJtgHburs/SvLNMdWyFCcD3510EQuY9hqnvT6Y/hqnvT6Y/hp/rr68f3FPXuz8pXytvH+of8NfG2TSuIJ+FljXc38tsLd3QlVtB7aP6fWHkmTnINePmKRpr3Ha64Ppr3Ha64Ppr3Ha64NjU+O4zoy9D9iY5LQkvwRcCOwY02tJko5iLB19VR1McilwF3PbK2+oqkfG8VqSpKMb2z76qroTuHNcX3/MpnJJ6TDTXuO01wfTX+O01wfTX+O01wfHoMapuB69JGl8vHqlJDXOoD+CJH+V5KEkDyb5TJIXT7qmwyX5QJJvdHXeluTESdfUK8kFSR5J8kySqdn5kOT8JN9MsjvJZZOu53BJbkiyP8nDk66lnyTrknw+ya7u//edk67pcEmek+SrSf6jq/EvJ11TP0mOS/K1JHeM83UM+iP7QFW9oqo2AXcAfzHpgvq4G3h5Vb0C+E/g8gnXc7iHgT8A7p10IfN6Ls/xGuB04KIkp0+2qmf5CHD+pIs4ioPAu6vqpcBZwCVT+G/4NHBuVb0S2AScn+SsCdfUzzuBXeN+EYP+CKrqhz13n8dhJ3xNg6r6TFUd7O5+mbnzFaZGVe2qqmk6EQ56Ls9RVT8B5i/PMTWq6l7g+5Ou40iqal9VPdDdfoq5oFoz2ap+Xs35UXf3+O5jqt7DSdYCrwP+edyvZdAfRZKrkjwG/DHT2dH3+jPg3yZdxDLQ7/IcUxVSy0mSDcAZwFcmW8mzdcsiDwL7gburatpq/Fvgz4Fnxv1CKzrok3w2ycN9PjYDVNV7q2odcDNw6TTW2M15L3O/Tt88jfVNmQUvz6HBJHk+8EngXYf9BjwVqupQt/S6FjgzycsnXdO8JK8H9lfV/cfi9Vb0Hx6pqlcNOPWjwKeBK8dYTl8L1ZhkC/B64LyawF7ZRfwbTosFL8+hhSU5nrmQv7mqPjXpeo6mqp5M8gXmjntMywHus4E3JHkt8Bzgl5P8a1X9yThebEV39EeTZGPP3TcA35hULUfS/XGX9wBvqKofT7qeZcLLcwwpSYDrgV1V9aFJ19NPklXzu9CSPBd4FVP0Hq6qy6tqbVVtYO578HPjCnkw6I/m6m4J4iHg1cwdHZ82fw+8ALi72wb6T5MuqFeSNyWZBX4X+HSSuyZdU3fwev7yHLuAW6ft8hxJPgZ8CfjNJLNJtk66psOcDVwMnNt93z3YdabTZDXw+e79ex9za/Rj3cI4zTwzVpIaZ0cvSY0z6CWpcQa9JDXOoJekxhn0ktQ4g16SGmfQS1LjDHpJatz/A/mOynkfzZAHAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.hist(r, bins=100)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "r = 10*np.random.randn(10000) + 5\n",
+    "plt.hist(r, bins=100)\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "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",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

section_5/25_sampling_from_gaussian_distribution_spherical_and_eliptical.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "from scipy.stats import norm\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "r = np.random.randn(10000, 2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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TpaU2nyUFUoTqQuX6dCYp7Gonr6qnAgEfWGbh3Vp9kbHco0iou427APDkmct4/tzbbaFDr1JfL8MNeBtipwid/T5+yHYQbtJSm8+GPUWkZbVnmJW9Fia+du+ix1QJ+3nRbAby+MhAqxJmy+hJz4S67HfTtbrU0Kri6CrDTQuv2btt3aIGIjKChE+cOwVZWClNrQBZKyYmdLLzOs2ks8LSngKEEImKaDHRsHu72t76yl4LN+sNpZqnnayP2pGLAOza3I9TF6eUBvTQjo0AgD1HJ6WLhF1lM/Do931Dj0GqbJwkUfoYex17ELrFsDtFuVQXp9szMdWmLmmCqgsy6SLs9xe10XeQ9zm97x6sUTQbsY21qmRSNlYWiE0EjJHjFuWS9c5062i4NcizDBv1bBP2+4trx2mHLVX3ii194BfzTlP4xCRs2DuEjiiXLKY+PFjJjPfAMElhG2xVp62GENj/7HlsXd/X9nu7hK9SLuVWnoCTpx1CJxHq5U2UPSQCGKbbscsjbaP88DPn2qp2avUGTl2cwqEdG7tOSIwNe4fwq3n12wIe3L7BU38lTCyThbqYtFEuWfiHm3Paevs2T794BU+dudwy1PMe/WF11FHzBodiOoRsiyjbAqp6QQ4PVrCy15KOrdM82nL16ixZRXz9C3fh9RDZf4bpBEUiTB64F1///F2LrvVyycKDm/s9c00NIRbVopcV90pa6srjhqtiOohfOZSfLOnYRBV7v3VukXKeDrYgkfO9t67vw/Pn3ubwDhMKInSkebafoxGkBFin8izrcLljBtCRJVX1i1Th1F131iAzTNooEuHVQ59e9JjbGVrzS6VAjWDiVluMm9jUHZnwqBKszsenAxj1yoJnfuxstbULYKPOpJUvfnL1op9lWklB80i2Ue/2yjI27AmiI0uqIzwE3LqYt4yezMUBJyb/vDb1XmvXanJn+dZ0LfGGGEnDhj1mnBdcudeCVaC27jPOapmt6/u0uhzNzM5hbKLKejNMZjj96tXW/5vcWa4oWUZ12LMIV8XEiPM0qkBTVhfUrAIgyA9MnLo4JR3LrZN8babuWR3AMN1AySqCCEo5326BPfYYkZ1GrTcEli/tweSBppKeXf7o13FG5t+wxC+TdwoAVD27CMDOTRU8pdjhdtNulj32GPFLlro9+rwoPTKMCcolCys8dqQCzR2uqna9m2rajXjsRPTnAD4D4B0hxJ0mxswKQZI0Kg+8QIS1+44rG/0yDKPX+eut6RoeHxnwbKnXDZgKxfwFgG8A+O+GxssEXj0XgfaWXqoOLLYxZ6POMNFYVS75ttTrBowdUCKiNQCe1/HY83JASXXAaPmSImZmG8rmAPYFZ9JD54NITLeT98NJQAr12InoISIaJ6LxqSl5pUfWUMXMr7uMOrC4BdfpfffgtdH7lcJFQVnZa+HrX7gLVoF7ijPdi3032TtnW3fJjUqfKU/EZtiFEE8IIYaEEEN9fe0dybNI0GSMeyEwlcyZrtWx5+gk3resByUNgTCGyTuq8kZZgYLXIpBV2ApEQCXyr8JtyIO+XoUQaNXF1xT9KBmm26gunEB1Iis5zmONO9exuwhS5eIl8i/DnZV3J3lWhNSmZhhGjvvEqY4+UyeIW+LAiMdORE8D+BsA64joTSL6bRPjxk2YbdrwYEUrVr58SVH6RTpj7suX9rBRZxgJqt4Efri98SRq3JMI/xjx2IUQXzQxTqfQXS39tmmqMXSEumZmF48rm1M3nYxjGBluTXUbIcJ1DQMWe+OykuNO17h72ZVOee25j7EHWS1VhtV+jWoMu/+iF06PQDWnFSV9r6RIhAc397d1SmKYPPJurY6929aFut6d997wYAWHdmxEpVxS6jPpEKSyJonwT+5j7H6rpdNzVkFQiwoND1aUQl02bo9ANadlVgElq+ir92LXxI+/cRX1BodumPygOtuxomTh8IlLvte7rIuSLLcVxVP2OpgoG1dHnts0uffYvVZLt+esumRUj9tjey0KMo9A9fzpmToO7dgojSe6+6UCUIodMUxWkRl1q0C4PjvnG4YpWUXsWuiVGsUb9yNoZY2s+q3T4Z/ce+xeq6XsCwo6ttd7qDq5eM3J9ib88gJbRk9qtwtjmKxSJAIRMOvjqRcIsfU3DRpaSULiIPeG3StZsufopNYYK3st3KjPKxMuQRMyOs/32y5yopXpBhpCoKHhe80L4JHvBGumEbYEMUxoJWr4Jyi5D8V4JUt0Ylwlq4gDD2zwTLgMD1awc1MFRWoGTIpE2LlJ/UW657Sy18LSngL2HJ1sJWL8kjPdJEHKMDpcn21g77fPaZURRilB9AqtpEWuwJgIWBDiEgHzW5HdSRCgGc9737IeTM/UtVdx2Tglq4idm5qJVS+PQDUHEBYliuyEqf162esYhtFrZq0S8NNthC2zLQCkdsBkiEhXBCy3oRidzLWp2JcqmeLsVarKnEu7KkkOKbnrXp1z54YcDHMLnWbWUUsQZaEVWSP5Tterq8itYdc9FGAi9qV7McjeP0is3P1cZ6J1t2a+gGHyTrnXv5l1J0oQk5IrkJHbGHucH3KQi8F5MY1NVFEg/QMXqvfJo+40w4TlpqT3r+1U2THw6nStrSF81BLENLXky63HHuehAFVnJBUDj34f07W68vi0DK+LLm+SowwThRmFwqntudv3qYBecw7d6pkk5ApU5NZjj/NQgF3lUtT0vu3ejbpGvUikTMCMTVS1yzYZppspErU5X7ZRP73vHuX9pVs9Y0quwAS59djjPhRgj9uJSpX3L5N/TfZFxweVGGYxBWrWttt4SXV4hWeDCnjFXa+uIreGHUjmQ15mFVoXAlFTlS4q07U6dh+dxFeefQn/acfHFy1aXO7IMO3MC6DXKqBWn285daoKMq/wbJoSokHIpWGPImof9rWyuvIeIqAAY0JdM/V57P32udbPXObIMGpuzgm8Nnr/oseCxsCTEPAyQe4Me1DltbCvdS8AM7Nz0np0+2Tp9Ewd5V4L792Yk9ap61JvCBx87gJuznELPIbxwi0oFiY8m6aEaBBylzyN0tNQ97WyhMq1mbp0TAHgvZtzWFFqGvflS3ta6o1hldSna3UOwTCMD7JahuHBCvZuW4dV5RLemq61SiBVpCkhGgQjHjsR3QfgPwMoAvhTIcSoiXHDECUmpvvaoLHtekO0KmGma3WUrCKOjAy0xrJrajkJyuSFIgFJtwoo9bT7rWF29GlJiAYhssdOREUAfwzg1wB8DMAXiehjUccNS5RDArqvjZo4cWbVT++7B6+P3o/HRwZQDtBBiWHSTNJGHQBqknr2KDv6KMQtDmYiFHM3gJ8JIX4uhJgF8JcAPmtg3FBEqV/Xfa1qASiXLBQ04yvuhMzwYAWTB+7FkZEBVFKemGGYLCC7T5OockmimbUJw14BcMXx85sLjy2CiB4ionEiGp+a8m4lF4UoMTHd16oWgIPbN+ADy/S9bq8vlhA+Bs8wDDAzO6ctd93JKpckdgmRZXuJ6PMAtgkh/vXCz78B4G4hxL9TvSYu2V4TqMofVY+v3XdcO1ZOAB4fGWApXobpEG757BUlC9dn5xaVIOvICkRBZRMIaCvH9CNO2d43Aax2/Hw7gLcMjJs4fomWII1rZQhg0Xh84IhhzFKrN/DUmcstwzpdq8MqEFb2Wrg2s1ivKUhpdBCy2sz6JwA+SkRriWgJgF8H8JyBcRMnzBZq77Z1gUIozvHSfpqNYbKI21uuzwv0LulBpVxq+10nQiRJNLOObNiFEHMAvgTgBIBXADwjhLgQddw0ECbRMjxYwa7N/YHepzpdw9p9xwNJ+DJM3imXLFjFztwT1emacmdt2sFKohbeSB27EOJ7AL5nYqw0EXYLNXTHbYu6J+kg0H5SjmG6mXdr9UTOduiGSILIj3Az6xQRdgsVdStXJAIt/NcLq0B4cHN/2xwZJg8ENeomfHvdEEkSJYxBYMPugdcWyuvAgddW7sHN/S1JARXzoileNO/hwfdaBfQUCU+euYxavSE9Ps0waebIyIDvvaBLkSiyd+/V98CNKv928Ll0RKEzJQIWRbUxLLItlF+1jFdlzNAdt+HUxSmltgzQ9FS2jJ5EeSFzL8PdJYajOEzWOHziEg48sCFSiW+5ZOHm3LyRarJ5IbTticp5m67VMTZRTVyCIDMee6e2PmGO+vpVy3hVxtgLkx/V6RreuzHXseQRwySN7fx8on9FqNeXrCKIYKxEOEj5oddzOy1PoENmDHsnTm+FXSz8qmWGByvKbaG929ChPi+wfEmPdss9hska+589jx///Grg15VLFg7t2Ihpj52vk0q55CnVIYutezl9XnH4NJQtZ8awd0LjIexioXMsWXUR2SEk3YTnu7U6V8swuaVWbwQKI1bKJRwZGcDkgXtbYU8/bKOtuu/sRcIZPvFz+oYHK8r8QBqacGTGsJvSeHCuwn51rKoVe++2dbBcal9WgRat4l4VNcODFezcVNHyxDkUwzCL2XN0snU/yu4zq0gol6y2ggdZMYRzkXCi4/QdeGBD7AePdMlM8tREJxNdLZZV5ZJnghRAe22V62evbi1jE1UcO1v19cStAmE2DfqnDJMSbGfMvh93bqpgac+tPsMrey0ceGDDIkP91bHzePiZc2gIgSIRvvjJ1XhseGPr97KiDJ0IQZiOTHERWQQsDGFFwKJWxWwZPemr42IVCIc/f5ey8a0dYlH97vS+e4zMAwCWLyni+ixrxzDdQZjm7+4GNSWruCis8tWx89LDgg9u7sdjwxulzl7JKmKZVZBWpOne450iThGw2Ih6eksnHv++ZT0YHqxgz9HJwGPoxvt1n8dGnekmVq1otqsLYttVWi+2nXj6xSvtL1p4/LHhjcqQy9KeAkpWMXO9Tm0yE2M3gU483s6ye8X0Vb8rELVV1Mji9GlIrjBM2ghSMeaFczesCnfaj6ucrHdr9Uz2OrXpKsOuU41iX1heyU/VOA0hFmXOVZn1rev7tKpiyiULRd2WTAyTcVaVS9i6vi+yNICzKEFVoGA/7uXA2a0rXxu9H6f33ZMZow7k1LCrqlmcWXGgPf/p3Gp5yQnYv5NdNM7MuWqbd+ri1KKxV/ZabV+EVSAc3L4BjXlOnjLdwbXrN/GkQzs9LE4v/YufXC19jv14EpK6cZCpGLsOOs0xnB2LvJKxXjF9nTi8aptXna5hz9FJrCqX8PjIAABg77fPYd5ZAUPA+BvBD24wTFZxy2SExXmGxK5+efrFK9KqmDRXtkQhU1UxOqgqTjqRzfZ7L53qF68MfJGIDycxTADcVTF5Q7cqJnehmDi7kPtt43Ri+rV6Qyn0xUadYfTJWoKzk+QuFBNnf0G/bZz790HNNHvsTDfgrkUPSt699DBECsUQ0ecBHATwKwDuFkJoxVc6GYpRHThIwxevezAJaM75E/0r8ONXrybSRYZhskClQzHxJCTCdYjrgNLLAHYA+K8RxzFGmpMhMlkEGUUi7NxUwbGzVTbqDOOiZBVwaMfHpX0STNz3fgUYWcBI8pSIfgjgd9LgsaedsYkqdiuqaZyUSxama3qSpAzTLah23yodKJl2jB86BRhJefRdmzxNO8ODFU9daBs26gzTjkpWW3ZmBACuzdQDN+TxK8BIe79TQMOwE9EPiOhlyb/PBnkjInqIiMaJaHxqair8jHNAED32KLDkL5MWKuUSei0zfqTT8NqHEb1yV7oNeeyxVDEMuwCjE01/TOMbYxdCfMrEGwkhngDwBNAMxZgYM6s48wC6yVRdeq0CavX51vbw4HMX2PtnEufa9ZvGDiDZBlZXhhvwL3f2G8tZxhxnSXVYOBSTELYOxeuj92uFZnSZcRj14cEKG3UmFZgy6iWriK3r+7Bl9CR2H53U7ndqN4hXhUtUoRygvT7eVNOfThKpKoaIPgfgvwDoA3CciCaFENuMzCzHuBMva36pXa7UKhDqIXVi7Jjf+BtXI9cIM0xaKJcsfOauD+PY2WqoBtZe1S0qb5uAthPrJpr+dJpIHrsQ4jtCiNuFEEuFEP+Ijbo/ssTLaVetOgEYuXs1yiV5T0UdavUGnn7xCht1JjcsX9qDUxenQhl1G1UsPIgX7iUQmBZyd/I07Xht+WwEgFOhECOPAAAVg0lEQVQXp3Bw+wbtGKIMPrXKZAla2F6qrlpTMWzZOEG98KhNfzoNx9hjJkiXJbfMsAyvftg6zbIZJg0QgF2f7MdrHjknryY3QciqFx4E9thjRqVlI3ueFgI4MjLQ5m1YBcKSngK312MSo1yyQNTsSuZ33QsAx85WMXTHbb7es+x3S3sK0kIBWU/UrHrhQWDDHjM6sgJWkXD95hzW7Dvum/xcUbLaZBRWlCxcn51jo84kyvKlPS0jqlPjbce/7WSl18lO9++AdoNv3zu2mF6ndGXSSO702LOAuypm6/o+nLo4hbemayj3Wnjvxpx2RczKXgsTX7t30WNBxMYYppNYRQIEtK9nAvDa6P2h3su+r6rTNamnnuXQik1cImBMCLy2fFtGTyr12WVMS56bpoMSTHdTbwRzHKPE0O37SubY2LuBrBt2XdiwJ4CXgFBQo1zutVoXsr3lZB13JqtMz8xi7b7jkYS1wp4MTatUbxi4KiZm/ASEgnos12bqLe/ENuZs1Jmscn22EVlYK8zJ0CwIewWBDbsCWxBo7b7jnkeRg+InILR1fR+8ihSXL2mKh3EhI5MVwhqZsMJafi0rZWRB2CsIHIqR0Emhfa9t4thE1be5Rrl3Ccq94OQokxmKRcLSAqEWQi+mOl1rCzX6VbeEabaTBWGvILBhl+C1ekc17F49WXVOpWb1QmO6l3pD4Jffvwx7t61rVa0UCNAplCGgLdSo42gFrUmPs1dyHHAoRkInV2+vbaLO+KZO3zFMnNjX9szsHIB2o16yCm39A7zOcIQJk3iFV8OEb9IMG3YJYWU5deLyXkeX/ca3LzRVow5bQaBSLmHLR27zHItj9EycrChZ2P/seWUp7+ycwMivrl50X/g59EEcLb/kKEsKdAFhZDmDxOVV20SvU6myuKIqhjg2UcUen76quzb34+hPrgSuM2YYGUUizAvROvXsvK5KVhFE8AwzNoTAsbPVRcbU76BdkJ2rTniVJQVyTpDki/O0m5ugcfnhwQrG37iKp85clupbOMdRXYT2AuNlrivlEh4b3ojnz72tpa/Bmu6MH/NCtE6MyurB/RwNoP1+8XJ0goZJ8pYc9YMNuwKd1VunNVfQC+fUxak2I6qzQHgtMG7sG+JdRXclgabxd0oePHnmsu6fwHSYNB5Ac3rPsntH99p03i/uFpJRNF/ylhz1gw17BHSqWIJeOGE8iyC9H+2Gwl5NeyvlUlvXmGNn3wxUrqZb9cAEo2QV8Yn+FTj96tVY39dL80XHe967bR12a3jt7vtFNzzid2o0C12PTBK1Nd5hAA8AmAXwKoB/JYSYNjGxLODnjYe5cMJ4FjoLDNC8OXdsul27aa+TnZtuD+S1s1E3DwHYuamCo397Jfb3rjcEVvZa6F3So+09u43tR395Of7vO9c932fr+r7Ac9PJb4WpbQ9LGqQJonrsLwDYL4SYI6I/BLAfwO9Fn1Y28NKYDisRGsaz0An3rOy1cOCBDb5Ne7eu78PhE5ew5+jkIuVJPhCVPAJINCR2baaO3iU9IAAfWrHM8/qWGduSVcSWj9yGMz+/pgwlnbo4FXheuudO4kiOdvJwYxCi9jz9vhBibuHHMwBujz6l7KCqfT0yMoDT++4J9UWGKbvy8uYr5RKOjAxg4mv3Yniw4tm0d++2dTh2trqoJOzJM5fZqDMtnNfG3m+fayvptUt+dx+dlBrb1/++hlcPfVpZbhsmmZmmxGhapAlMxth/C8BRg+OlHtPbO/cW7vGRAa2xVMnNBzf347HhjYsei3rylekOdCqh6g2B//BMM24+PFgJVExgMpmZpsRoWhYZX8NORD8A8CHJrx4RQvzVwnMeATAH4CmPcR4C8BAA9Pf3h5psGjG1vYuyhVNtX52P+zUh0C1JY7oDgVvGveIRcpwXaF2nQYoJTCYz05QYTcsi4xuKEUJ8Sghxp+SfbdR/E8BnAOwSHu2YhBBPCCGGhBBDfX3BEyR5J8oWzs9LcJ66A27dtEDzpt25qYLDJy4FqlW3G2Vzw+z8Yht1d4WUG/s6DVJMYPKkpz1WuWS1HltmJXOoPi3SBFGrYu5DM1n6z4QQM2am1J1E2cL5eQmyRcO+aXV6sDohNE+t2iGetfuOa73ODy+vkEkOW3WUCPAqnbfDh0GKCUwnM2/O3SrHvTZTTyRpGWf1jRdRl7VvAHg/gBeIaJKI/sTAnLqSsPo0gL+X4LVo+FXJbPnIbYsSXXY3+bCNQWTYidtKTg+LZJlyb1Pjxe88lG3A3NchoZnrCVtMoEtakpZA07if3ncPXhu9v+N/t4qoVTH/RAixWggxsPDv35iaWLcRZQvnt631WjS8qmRO77sHr/99TXkS1p531GCMQPPGVImbMclxo97w3c05JS92bqq0OQJPnbmMr46d7+g805K0TAt88rSDBDmoEGYLpzu+V3JJddTbXgxUW2v7hrH1baLWV781XWs7Qp53lvYUFoUPOsHKXgs36vOhqp1KVsHztDEBbdedTBLDNu5Dd9zWMe81LUnLtMCGvUOEqXIJEnMMqiYJqBcNldEfm6gqy96cN8xjwxtx/KW3lZKsOtjjeXWazxPFAuEPd34cj373QqTPzQsCcP/HPwwAePrFK2gIgQIBRQL81CEI8DTqqqSqykO2d2WdMuxpqoxJA2zYO0QnuzCFGV+1aHgZfS89mes35xZ1kz/wwIZASVg37hswz8JjBGDz2pU4fOJSKKPeaxUwo6HbI4Cm/ADd6j40L/TkHvyeojKYXgnUToZF0pK0TAts2DtEp2N+JsdXGX2vsWy5X3uncGjHRhzasRFfefYlLaPjhLB4l2H3fs0rAsCPX70aWgp5SU8RAqS1iMpEu1QUibDMKuD6rPe4K3stpcG0z0P47fI6QZ701KPCHZQ6RJQqlzSMH2QsZzJVKFKpXglWtxFQVeqkvWS+Ui7hwc39WgngKBpp79bqrWS5SRpC+Br1klXEgQc2KH8/PFjBrs39bd93N4dFkoANe4fo9EGFOA5CBFHa8yudFFAfZnIbKGWc1oBi5PIl5qtunPpApy5OdVyWYVW51Cqpe330/ta/TpeL6h4iemx4Ix4fGchNm7kswqGYDtHpmF+nqmiczykEcJG9SidtGkKgZBV9E1xecdqo3KjPY/mSoq9nqoLQrO0Wouk5uz9HnVBYlI5UXou3LIFoFQggRGqBWLKKgQ0zh0WShTxUADrG0NCQGB8fj/19uxmZQJP7hg3SsMOJPY5fmaJ9avXUxSnfxSXoPFb2WvhFbU6rs5BVoECxZ5tyycLkgXs9n+NXzVMkwuZ/vFLaKOPBzf0YuuM2HHzugrRlYblk4eD2DYEXb+CWA1DutTA9U/ddWOwept2ehEwbRHRWCDHk+zw27N2ByuA4y9Z0Swzthgtu46xjkO3389s9jE1UlQZOxpGRAWXSTkZYr1lWu+3EbiTuNbaqtZ39uGpuYTxnGTrfEwGtHqZMetA17ByK6RJ0qmh0wgh28syvdNKr5E23483hE5e0DPuDm/tbz9cN4YR1Z2wtcq8zCV5jE6DcVdiPq15vqlxW53vq1oM9eYGTp12CThWN6jlFIu0kmJ3UUyXyVLrvMl0Pr4XGns+RkYGWIJkJeQNAr/pGNt+vjp33lT6Ouj+WfSZ2c4u1+45jy+jJlo6P6nHg1vd0ZGQgFWqEjFnYY+8SdE7mqZ4TZvuvGsvr4JHbaKmSqKpTj7a8wVNnLkcyoEI0+8MuX9KDd2vqeLS9+9DZKURJmDpxL76y3c+eo5P41vhl/PTyu74nk/lgTz5hw94l6NzAJittZGNtXd/nefDIbbTCHBN/bHgjhu64DQ8/c04rkaqi3hBYvrQHkwfuVeYeVpQs7STv4yMDgXIGMmwVTCcqSWZZctYZyklDw2Wmc7Bhzyl+BleFSb0a91hbRk8qjaDMYIf1JocHK0a6Qdk7CNUCQwQto15ZqDt/9LsXpL9fvqSIeeE/1q6FXIJsjrro5jiYbMOGPYfEdeMG1avxMkKqcE/QhcZZgy/z2GVtAZf2FKSetFOYDGhfYHQWD6eXPa3Qhbk+28CRkQHfXYa7f609xyA1/6vKJTz63Qsd1TFikoeTpzkkrqYDQfVqVMlZ26PVRZYUdLb/E1BXniyzCljZay1KBh/cvsE3gShrnuBXOWLX7fvp4tu52q9/4S7P5K87AQp4J4xlx/q3ru9TCo91q3Z5HmHDnkPiajoQVK9GJYOwdX2fsnrDjduA27sRmRcKAAWXdavV53GjPo/HFyQA7B1BmP6bqo5BWBjjcUfFjv18mRF2StrKdFZs7L/VXd2i0mbZtbm/7W9SNT4HuMQxT0Ttefr7AD4LYB7AOwD+pRDiLRMTY8ITtemAiQYeMrwSqrphI9VuRBWflh0wlYUdwhyBD5oDGB6sYLcifGMvunbyV1VpI5u78zV+81C9P6CW4mWyR6STp0T0ASHELxb+/98D+JhOezw+edpZdOQDTL02anWFzolYJ2v3HTdSNpjUyUrV3ys7wu/1tx4ZGQgVD//I/u8pcw980jT9xHLy1DbqCyyHmVJdJiJRapNNNfDQJUycXmYYyyULN+fm2xYkv8SojcnyP2dtuy0TUFkYU7bLAW7lBJw7Fq/EaNhkuCr30K03bl7LPiPH2InoD4joCoBdAL4WfUqMCWTJPh3ibgpsKk5/cPsGaZz8M3d9WDqOU5JYFbf3ivWrcI4FyA22c54yKWN7IfVq7h02Ga46ERxF8tfrhGuaMfm9pw1fw05EPyCilyX/PgsAQohHhBCrATwF4Ese4zxERONEND41pU7gMMkSRwMP4JYxqE7X2hJ/BLUWvCzRuXNTUyfGLj90JkZVyULn4yariLw06Z07H3vRnVd40HZz70M72kscnc8Jimkd/ywbx7iqx5LA17ALIT4lhLhT8u+vXE/9JoCdHuM8IYQYEkIM9fXpN3Bg4iWOBh5ur1bW1f7Y2arSODgN495t63DsbFVpWKKIn4UxnH6vkckmyHA+rqqSCbPYhq0AUpFl4xj37jROIoViiOijjh+3A7gYbTpM0qhufADGttteXq2NrnHwMyxRxM/CGE6/18hkE9wLqVWkVrPwh585J41/y+QFdBkerGDvtnWt5iiHT1wK/X1m2TjGtTtNgqgx9tGFsMxLAO4F8GUDc2I6QJA4qDs+D8Dodlv3ptd5np9h0dmBmNyleMXFVbIJzoV0Za8FiGazcK+DVgLhTxGbDJ9k2TjGsTtNiqhVMcrQC5MeokoMBK2UUc3B77i/Gx3j4Fez3ynxM9Xftmoh5n/q4pS0KsavsmjL6EnlyVAnUZKdJr5PmzBCbWkhz8qWrBXTBUS9kaNut90Li45R1zUOOobFtPiZE9mieexsNXTcWrfZSRTDaTJ8knXjmNferGzYu4CoN3LUk6yqmLrzUM7W9X2+vVBlJG1YTHq/gPqzNtmDNOr36SavxjHLsGHvAqLeyFG326oFZF4II6cdO2FYdA+umE4emmx2EvQ9shA+YfRgEbAuIGqSKGqJXNYSbEGSi6b/NtPliEm9B5MskbRiwsJaMfGT5NHpKNo1SRBEvyZrfxuTbWLRimGyQ5Jx0KTj4EEJEl7J2t/GdAds2JlAhPX8s5RgC5qTyNLfxnQHHGNntMmyLkgQ8nxwhekO2LAz2mRZFyQInFxksg6HYhhtsqwLEhST4ZW8an4z6YUNO6PF2ERVKQWQ1rLFNBBVzoFhwsChGMYX2zjJjDrHnr3plvAVky7YsDO+eEkCcOzZm24KXzHpgQ0744uXJAAbdW+yduqWyQds2Blf2DiFh0snmSRgw874wsYpPFw6ySQBV8UwvvCx+WjwyVQmbowYdiL6HQCHAfQJIf7OxJhMumDjxDDZIXIohohWA/gXAC5Hnw7DMAwTFRMx9scB/C4gbabOMAzDxEwkw05E2wFUhRDnDM2HYRiGiYhvjJ2IfgDgQ5JfPQLgKwDu1XkjInoIwEMA0N/fH2CKDMMwTBBCd1Aioo0A/ieAmYWHbgfwFoC7hRD/z+u13EGJYRgmOLodlIy1xiOi1wEM6VTFENEUgDcUv/4ggLRX1vAczZGFefIczZCFOQLpnucdQog+vyclUsfuNTEiGtdZkZKE52iOLMyT52iGLMwRyM48vTBm2IUQa0yNxTAMw4SHJQUYhmFyRhoN+xNJT0ADnqM5sjBPnqMZsjBHIDvzVGIsecowDMOkgzR67AzDMEwEUm3Yieh3iEgQ0QeTnosbIvp9InqJiCaJ6PtEtCrpObkhosNEdHFhnt8honLSc3JDRJ8nogtENE9EqapEIKL7iOgSEf2MiPYlPR8ZRPTnRPQOEb2c9FxUENFqIjpFRK8sfNdfTnpObohoGRH9LRGdW5jjo0nPKQqpNewZEBc7LIT4uBBiAMDzAL6W9IQkvADgTiHExwH8HwD7E56PjJcB7ADwo6Qn4oSIigD+GMCvAfgYgC8S0ceSnZWUvwBwX9KT8GEOwMNCiF8BsBnAv03hZ3kTwD1CiLsADAC4j4g2Jzyn0KTWsCPl4mJCiF84flyOFM5TCPF9IcTcwo9n0DwdnCqEEK8IIdLY2fluAD8TQvxcCDEL4C8BfDbhObUhhPgRgKtJz8MLIcTbQoifLvz/PwB4BUCqNKBFk/cWfrQW/qXuntYllYY9K+JiRPQHRHQFwC6k02N38lsA/kfSk8gQFQBXHD+/iZQZoyxCRGsADAJ4MdmZtENERSKaBPAOgBeEEKmboy6JdVAyJS7WSbzmKIT4KyHEIwAeIaL9AL4E4ECsE4T/HBee8wia2+Gn4pybjc4cUwhJHsusB5cGiOh9AI4B2O3a8aYCIUQDwMBCLuo7RHSnECK1uQsvEjPsQohPyR5fEBdbC+AcEQHN8MFPichXXMw0qjlK+CaA40jAsPvNkYh+E8BnAPxzkVBta4DPMU28CWC142db5I4JARFZaBr1p4QQzyY9Hy+EENNE9EM0cxeZNOypC8UIIc4LIX5ZCLFmQabgTQCfiNuo+0FEH3X8uB3AxaTmooKI7gPwewC2CyFm/J7PLOInAD5KRGuJaAmAXwfwXMJzyiTU9ND+DMArQog/Sno+Moioz64aI6ISgE8hhfe0Lqkz7BlilIheJqKX0Awbpa6EC8A3ALwfwAsLZZl/kvSE3BDR54joTQD/FMBxIjqR9JwAYCHp/CUAJ9BM9j0jhLiQ7KzaIaKnAfwNgHVE9CYR/XbSc5KwBcBvALhn4TqcJKJPJz0pFx8GcGrhfv4JmjH25xOeU2j45CnDMEzOYI+dYRgmZ7BhZxiGyRls2BmGYXIGG3aGYZicwYadYRgmZ7BhZxiGyRls2BmGYXIGG3aGYZic8f8B5jaimAmUQ7EAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.scatter(r[:,0], r[:,1])\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "r[:,1] = 5*r[:,1] + 2\n",
+    "plt.scatter(r[:,0], r[:,1])\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.scatter(r[:,0], r[:,1])\n",
+    "plt.axis('equal')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "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",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

section_5/26_sampling_from_a_general_multivariate_normal.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from scipy.stats import multivariate_normal as mvn\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cov = np.array([[1, 0.8], [0.8, 3]])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "mu = np.array([0,2])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "r = mvn.rvs(mean=mu, cov=cov, size=1000)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.scatter(r[:,0], r[:,1])\n",
+    "plt.axis('equal')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "r = np.random.multivariate_normal(mean=mu, cov=cov, size=1000)\n",
+    "plt.scatter(r[:,0], r[:,1])\n",
+    "plt.axis('equal')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "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",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}