ArtStudies/Probabilités/TP2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f9a51919-f7c1-4a14-a921-f908e6e0f3d3",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import scipy.stats as scs\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy.random as random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d68b921d-3512-4e16-a46d-c21d4a609804",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f79a2509060>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = [2, -2, 1, -2, 1]\n",
    "B = [1, 3, 2, 6, 3]\n",
    "plt.step(A, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "203d4fd9-f1c4-4a31-8ac7-dc87a34ad473",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def bernouilli(p):\n",
    "    plt.step([-1, 0, 1, 1, 2], [0, 0, 1-p, 1, 1], label=f'p={p}')\n",
    "    plt.legend()\n",
    "    \n",
    "for p in [0.2, 0.5, 0.7]:\n",
    "    bernouilli(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "43c17c05-8468-4469-abda-fbc9d6b85b38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiMAAAGdCAYAAADAAnMpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAfSElEQVR4nO3de2zV9f3H8dehl1Nw9DhACkit1SkXyZwcFFrsnAqHFUdC4m90MePiILGbSkqnG8gvqI1JdVGGFy4SQWKCrFPAkawTTjIFFDSjO7hLmTphtEprUzZ7KriWls/vD36ceGwL/R5a3z3l+UjOH+fL53v6+Xj42Cffc9rjc845AQAAGBlgPQEAAHBxI0YAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAICpVOsJdMfp06d17NgxDR48WD6fz3o6AACgG5xzam5u1qhRozRgQNfXP5IiRo4dO6bs7GzraQAAgATU1tZq9OjRXf55UsTI4MGDJZ1ZTGZmpvFsAABAd0SjUWVnZ8e+j3clKWLk7EszmZmZxAgAAEnmfG+x4A2sAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMCU5xjZs2ePZs2apVGjRsnn8+m111477zm7d+9WMBhURkaGrrrqKq1bty6RuQIAgH7Ic4ycOHFC119/vZ577rlujT9y5IhmzpypgoICRSIRPfTQQ1q8eLG2bt3qebIAAKD/8fzZNIWFhSosLOz2+HXr1umKK67QqlWrJEnjxo3TgQMH9OSTT+rOO+/0+uUB9DPOOX1xqt16GsBFb2Baynk/Q6a39PoH5e3fv1+hUCju2IwZM7RhwwadOnVKaWlpHc5paWlRS0tL7H40Gu3taQIw4JzT/6zbr6qj/7GeCnDRqy6boUHpNp+f2+tvYK2vr1dWVlbcsaysLLW1tamxsbHTc8rLyxUIBGK37Ozs3p4mAANfnGonRAD0/pURqeNHBzvnOj1+1rJly1RaWhq7H41GCRKgnzvwv9M0KD3FehrARWtgmt3+6/UYGTFihOrr6+OONTQ0KDU1VUOHDu30HL/fL7/f39tTA9CHDEpPMbtEDMBWr79Mk5eXp3A4HHds165dmjRpUqfvFwEAABcXzzHy+eef6+DBgzp48KCkMz+6e/DgQdXU1Eg68xLLvHnzYuOLi4t19OhRlZaW6tChQ9q4caM2bNigBx54oGdWAAAAkprna6IHDhzQrbfeGrt/9r0d8+fP16ZNm1RXVxcLE0nKzc1VZWWllixZotWrV2vUqFF65pln+LFeAAAgKYEY+d73vhd7A2pnNm3a1OHYLbfcoj//+c9evxQAALgI8Nk0AADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMBUQjGyZs0a5ebmKiMjQ8FgUHv37j3n+M2bN+v666/XoEGDNHLkSN199906fvx4QhMGAAD9i+cYqaioUElJiZYvX65IJKKCggIVFhaqpqam0/FvvfWW5s2bp4ULF+rvf/+7XnnlFf3pT3/SokWLLnjyAAAg+XmOkZUrV2rhwoVatGiRxo0bp1WrVik7O1tr167tdPw777yjK6+8UosXL1Zubq5uvvlm3XPPPTpw4MAFTx4AACQ/TzHS2tqqqqoqhUKhuOOhUEj79u3r9Jz8/Hx9/PHHqqyslHNOn376qV599VXdcccdXX6dlpYWRaPRuBsAAOifPMVIY2Oj2tvblZWVFXc8KytL9fX1nZ6Tn5+vzZs3q6ioSOnp6RoxYoQuvfRSPfvss11+nfLycgUCgdgtOzvbyzQBAEASSegNrD6fL+6+c67DsbOqq6u1ePFirVixQlVVVXr99dd15MgRFRcXd/n4y5YtU1NTU+xWW1ubyDQBAEASSPUyeNiwYUpJSelwFaShoaHD1ZKzysvLNXXqVD344IOSpG9/+9u65JJLVFBQoMcee0wjR47scI7f75ff7/cyNQAAkKQ8XRlJT09XMBhUOByOOx4Oh5Wfn9/pOSdPntSAAfFfJiUlRdKZKyoAAODi5vllmtLSUr3wwgvauHGjDh06pCVLlqimpib2ssuyZcs0b9682PhZs2Zp27ZtWrt2rQ4fPqy3335bixcv1k033aRRo0b13EoAAEBS8vQyjSQVFRXp+PHjKisrU11dnSZMmKDKykrl5ORIkurq6uJ+58iCBQvU3Nys5557Tj//+c916aWX6rbbbtMTTzzRc6sAAABJy+eS4LWSaDSqQCCgpqYmZWZmWk8HQA852dqm8St2SpKqy2ZoULrnfx8B6MO6+/2bz6YBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgihgBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgihgBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgihgBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgihgBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgihgBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgihgBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgihgBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgihgBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgihgBAACmiBEAAGAqoRhZs2aNcnNzlZGRoWAwqL17955zfEtLi5YvX66cnBz5/X5dffXV2rhxY0ITBgAA/Uuq1xMqKipUUlKiNWvWaOrUqXr++edVWFio6upqXXHFFZ2eM2fOHH366afasGGDvvWtb6mhoUFtbW0XPHkAAJD8PMfIypUrtXDhQi1atEiStGrVKu3cuVNr165VeXl5h/Gvv/66du/ercOHD2vIkCGSpCuvvPLCZg0AAPoNTy/TtLa2qqqqSqFQKO54KBTSvn37Oj1nx44dmjRpkn71q1/p8ssv17XXXqsHHnhAX3zxRZdfp6WlRdFoNO4GAAD6J09XRhobG9Xe3q6srKy441lZWaqvr+/0nMOHD+utt95SRkaGtm/frsbGRv3sZz/Tv//97y7fN1JeXq5HH33Uy9QAAECSSugNrD6fL+6+c67DsbNOnz4tn8+nzZs366abbtLMmTO1cuVKbdq0qcurI8uWLVNTU1PsVltbm8g0AQBAEvB0ZWTYsGFKSUnpcBWkoaGhw9WSs0aOHKnLL79cgUAgdmzcuHFyzunjjz/WNddc0+Ecv98vv9/vZWoAACBJeboykp6ermAwqHA4HHc8HA4rPz+/03OmTp2qY8eO6fPPP48d++CDDzRgwACNHj06gSkDAID+xPPLNKWlpXrhhRe0ceNGHTp0SEuWLFFNTY2Ki4slnXmJZd68ebHxd911l4YOHaq7775b1dXV2rNnjx588EH95Cc/0cCBA3tuJQAAICl5/tHeoqIiHT9+XGVlZaqrq9OECRNUWVmpnJwcSVJdXZ1qampi47/xjW8oHA7r/vvv16RJkzR06FDNmTNHjz32WM+tAgAAJC2fc85ZT+J8otGoAoGAmpqalJmZaT0dAD3kZGubxq/YKUmqLpuhQeme/30EoA/r7vdvPpsGAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAqVTrCVhyzumLU+3W0wAuWidb2X8ALuIYcc7pf9btV9XR/1hPBQCAi9pF+zLNF6faCRGgj5iU800NTEuxngYAIxftlZEvO/C/0zQonf8RAlYGpqXI5/NZTwOAEWJE0qD0FA1K5z8FAAAWLtqXaQAAQN9AjAAAAFPECAAAMEWMAAAAU8QIAAAwRYwAAABTxAgAADBFjAAAAFPECAAAMEWMAAAAU8QIAAAwRYwAAABTxAgAADBFjAAAAFPECAAAMEWMAAAAU8QIAAAwRYwAAABTxAgAADBFjAAAAFPECAAAMEWMAAAAU8QIAAAwRYwAAABTxAgAADBFjAAAAFPECAAAMJVQjKxZs0a5ubnKyMhQMBjU3r17u3Xe22+/rdTUVH3nO99J5MsCAIB+yHOMVFRUqKSkRMuXL1ckElFBQYEKCwtVU1NzzvOampo0b9483X777QlPFgAA9D+eY2TlypVauHChFi1apHHjxmnVqlXKzs7W2rVrz3nePffco7vuukt5eXkJTxYAAPQ/nmKktbVVVVVVCoVCccdDoZD27dvX5XkvvviiPvroIz388MPd+jotLS2KRqNxNwAA0D95ipHGxka1t7crKysr7nhWVpbq6+s7PefDDz/U0qVLtXnzZqWmpnbr65SXlysQCMRu2dnZXqYJAACSSEJvYPX5fHH3nXMdjklSe3u77rrrLj366KO69tpru/34y5YtU1NTU+xWW1ubyDQBAEAS6N6liv83bNgwpaSkdLgK0tDQ0OFqiSQ1NzfrwIEDikQiuu+++yRJp0+flnNOqamp2rVrl2677bYO5/n9fvn9fi9TAwAAScrTlZH09HQFg0GFw+G44+FwWPn5+R3GZ2Zm6q9//asOHjwYuxUXF2vMmDE6ePCgJk+efGGzBwAASc/TlRFJKi0t1dy5czVp0iTl5eVp/fr1qqmpUXFxsaQzL7F88skneumllzRgwABNmDAh7vzhw4crIyOjw3EAAHBx8hwjRUVFOn78uMrKylRXV6cJEyaosrJSOTk5kqS6urrz/s4RAACAs3zOOWc9ifOJRqMKBAJqampSZmZmjzzmydY2jV+xU5JUXTZDg9I9dxkAADiH7n7/5rNpAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYIkYAAIApYgQAAJgiRgAAgCliBAAAmCJGAACAKWIEAACYSihG1qxZo9zcXGVkZCgYDGrv3r1djt22bZumT5+uyy67TJmZmcrLy9POnTsTnjAAAOhfPMdIRUWFSkpKtHz5ckUiERUUFKiwsFA1NTWdjt+zZ4+mT5+uyspKVVVV6dZbb9WsWbMUiUQuePIAACD5+ZxzzssJkydP1sSJE7V27drYsXHjxmn27NkqLy/v1mNcd911Kioq0ooVK7o1PhqNKhAIqKmpSZmZmV6m26WTrW0av+LMFZrqshkalJ7aI48LAADO6O73b09XRlpbW1VVVaVQKBR3PBQKad++fd16jNOnT6u5uVlDhgzpckxLS4ui0WjcDQAA9E+eYqSxsVHt7e3KysqKO56VlaX6+vpuPcZTTz2lEydOaM6cOV2OKS8vVyAQiN2ys7O9TBMAACSRhN7A6vP54u475zoc68yWLVv0yCOPqKKiQsOHD+9y3LJly9TU1BS71dbWJjJNAACQBDy9UWLYsGFKSUnpcBWkoaGhw9WSr6qoqNDChQv1yiuvaNq0aecc6/f75ff7vUwNAAAkKU9XRtLT0xUMBhUOh+OOh8Nh5efnd3neli1btGDBAr388su64447EpspAADolzz/CElpaanmzp2rSZMmKS8vT+vXr1dNTY2Ki4slnXmJ5ZNPPtFLL70k6UyIzJs3T08//bSmTJkSu6oycOBABQKBHlwKAABIRp5jpKioSMePH1dZWZnq6uo0YcIEVVZWKicnR5JUV1cX9ztHnn/+ebW1tenee+/VvffeGzs+f/58bdq06cJXAAAAkprn3zNigd8zAgBA8umV3zMCAADQ04gRAABgihgBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgihgBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgihgBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgihgBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgihgBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgihgBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgihgBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgihgBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgihgBAACmiBEAAGCKGAEAAKaIEQAAYIoYAQAApogRAABgKqEYWbNmjXJzc5WRkaFgMKi9e/eec/zu3bsVDAaVkZGhq666SuvWrUtosgAAoP/xHCMVFRUqKSnR8uXLFYlEVFBQoMLCQtXU1HQ6/siRI5o5c6YKCgoUiUT00EMPafHixdq6desFTx4AACQ/n3POeTlh8uTJmjhxotauXRs7Nm7cOM2ePVvl5eUdxv/yl7/Ujh07dOjQodix4uJivffee9q/f3+3vmY0GlUgEFBTU5MyMzO9TLdLJ1vbNH7FTklSddkMDUpP7ZHHBQAAZ3T3+7enKyOtra2qqqpSKBSKOx4KhbRv375Oz9m/f3+H8TNmzNCBAwd06tSpTs9paWlRNBqNuwEAgP7JU4w0Njaqvb1dWVlZccezsrJUX1/f6Tn19fWdjm9ra1NjY2On55SXlysQCMRu2dnZXqYJAACSSEJvYPX5fHH3nXMdjp1vfGfHz1q2bJmamppit9ra2kSmeU4D01JUXTZD1WUzNDAtpccfHwAAdI+nN0oMGzZMKSkpHa6CNDQ0dLj6cdaIESM6HZ+amqqhQ4d2eo7f75ff7/cyNc98Ph/vEwEAoA/wdGUkPT1dwWBQ4XA47ng4HFZ+fn6n5+Tl5XUYv2vXLk2aNElpaWkepwsAAPobzy/TlJaW6oUXXtDGjRt16NAhLVmyRDU1NSouLpZ05iWWefPmxcYXFxfr6NGjKi0t1aFDh7Rx40Zt2LBBDzzwQM+tAgAAJC3Pr1MUFRXp+PHjKisrU11dnSZMmKDKykrl5ORIkurq6uJ+50hubq4qKyu1ZMkSrV69WqNGjdIzzzyjO++8s+dWAQAAkpbn3zNioTd+zwgAAOhdvfJ7RgAAAHoaMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwFRSfGzt2V8SG41GjWcCAAC66+z37fP9svekiJHm5mZJUnZ2tvFMAACAV83NzQoEAl3+eVJ8Ns3p06d17NgxDR48WD6fr8ceNxqNKjs7W7W1tf32M2/6+xpZX/Lr72vs7+uT+v8aWV/inHNqbm7WqFGjNGBA1+8MSYorIwMGDNDo0aN77fEzMzP75V+wL+vva2R9ya+/r7G/r0/q/2tkfYk51xWRs3gDKwAAMEWMAAAAUxd1jPj9fj388MPy+/3WU+k1/X2NrC/59fc19vf1Sf1/jayv9yXFG1gBAED/dVFfGQEAAPaIEQAAYIoYAQAApogRAABgqt/FyJo1a5Sbm6uMjAwFg0Ht3bv3nON3796tYDCojIwMXXXVVVq3bl2HMVu3btX48ePl9/s1fvx4bd++vbemf15e1rdt2zZNnz5dl112mTIzM5WXl6edO3fGjdm0aZN8Pl+H23//+9/eXkqnvKzvzTff7HTu//jHP+LG9aXnT/K2xgULFnS6xuuuuy42pi89h3v27NGsWbM0atQo+Xw+vfbaa+c9J5n2oNf1JeMe9LrGZNuHXteXbHuwvLxcN954owYPHqzhw4dr9uzZev/99897nvU+7FcxUlFRoZKSEi1fvlyRSEQFBQUqLCxUTU1Np+OPHDmimTNnqqCgQJFIRA899JAWL16srVu3xsbs379fRUVFmjt3rt577z3NnTtXc+bM0bvvvvt1LSvG6/r27Nmj6dOnq7KyUlVVVbr11ls1a9YsRSKRuHGZmZmqq6uLu2VkZHwdS4rjdX1nvf/++3Fzv+aaa2J/1peeP8n7Gp9++um4tdXW1mrIkCH64Q9/GDeurzyHJ06c0PXXX6/nnnuuW+OTbQ96XV+y7UHJ+xrPSpZ96HV9ybYHd+/erXvvvVfvvPOOwuGw2traFAqFdOLEiS7P6RP70PUjN910kysuLo47NnbsWLd06dJOx//iF79wY8eOjTt2zz33uClTpsTuz5kzx33/+9+PGzNjxgz3ox/9qIdm3X1e19eZ8ePHu0cffTR2/8UXX3SBQKCnpnhBvK7vjTfecJLcf/7zny4fsy89f85d+HO4fft25/P53L/+9a/Ysb70HH6ZJLd9+/Zzjkm2Pfhl3VlfZ/ryHvyq7qwxGffhWYk8h8m0B51zrqGhwUlyu3fv7nJMX9iH/ebKSGtrq6qqqhQKheKOh0Ih7du3r9Nz9u/f32H8jBkzdODAAZ06deqcY7p6zN6SyPq+6vTp02pubtaQIUPijn/++efKycnR6NGj9YMf/KDDv9q+DheyvhtuuEEjR47U7bffrjfeeCPuz/rK8yf1zHO4YcMGTZs2TTk5OXHH+8JzmIhk2oM9oS/vwQuVLPvwQiXbHmxqapKkDn/nvqwv7MN+EyONjY1qb29XVlZW3PGsrCzV19d3ek59fX2n49va2tTY2HjOMV09Zm9JZH1f9dRTT+nEiROaM2dO7NjYsWO1adMm7dixQ1u2bFFGRoamTp2qDz/8sEfnfz6JrG/kyJFav369tm7dqm3btmnMmDG6/fbbtWfPntiYvvL8SRf+HNbV1ekPf/iDFi1aFHe8rzyHiUimPdgT+vIeTFSy7cMLkWx70Dmn0tJS3XzzzZowYUKX4/rCPkyKT+31wufzxd13znU4dr7xXz3u9TF7U6Jz2bJlix555BH97ne/0/Dhw2PHp0yZoilTpsTuT506VRMnTtSzzz6rZ555pucm3k1e1jdmzBiNGTMmdj8vL0+1tbV68skn9d3vfjehx/w6JDqfTZs26dJLL9Xs2bPjjve159CrZNuDiUqWPehVsu7DRCTbHrzvvvv0l7/8RW+99dZ5x1rvw35zZWTYsGFKSUnpUGkNDQ0dau6sESNGdDo+NTVVQ4cOPeeYrh6ztySyvrMqKiq0cOFC/fa3v9W0adPOOXbAgAG68cYbv/aiv5D1fdmUKVPi5t5Xnj/pwtbonNPGjRs1d+5cpaenn3Os1XOYiGTagxciGfZgT+rL+zBRybYH77//fu3YsUNvvPGGRo8efc6xfWEf9psYSU9PVzAYVDgcjjseDoeVn5/f6Tl5eXkdxu/atUuTJk1SWlraOcd09Zi9JZH1SWf+NbZgwQK9/PLLuuOOO877dZxzOnjwoEaOHHnBc/Yi0fV9VSQSiZt7X3n+pAtb4+7du/XPf/5TCxcuPO/XsXoOE5FMezBRybIHe1Jf3oeJSpY96JzTfffdp23btumPf/yjcnNzz3tOn9iHPfI22D7iN7/5jUtLS3MbNmxw1dXVrqSkxF1yySWxdz0vXbrUzZ07Nzb+8OHDbtCgQW7JkiWuurrabdiwwaWlpblXX301Nubtt992KSkp7vHHH3eHDh1yjz/+uEtNTXXvvPNOn1/fyy+/7FJTU93q1atdXV1d7PbZZ5/FxjzyyCPu9ddfdx999JGLRCLu7rvvdqmpqe7dd9/t8+v79a9/7bZv3+4++OAD97e//c0tXbrUSXJbt26NjelLz59z3td41o9//GM3efLkTh+zLz2Hzc3NLhKJuEgk4iS5lStXukgk4o4ePeqcS/496HV9ybYHnfO+xmTbh17Xd1ay7MGf/vSnLhAIuDfffDPu79zJkydjY/riPuxXMeKcc6tXr3Y5OTkuPT3dTZw4Me7HmebPn+9uueWWuPFvvvmmu+GGG1x6erq78sor3dq1azs85iuvvOLGjBnj0tLS3NixY+M22dfNy/puueUWJ6nDbf78+bExJSUl7oorrnDp6enusssuc6FQyO3bt+9rXFE8L+t74okn3NVXX+0yMjLcN7/5TXfzzTe73//+9x0esy89f855/zv62WefuYEDB7r169d3+nh96Tk8+2OeXf2dS/Y96HV9ybgHva4x2fZhIn9Hk2kPdrY2Se7FF1+MjemL+9D3/5MHAAAw0W/eMwIAAJITMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABMESMAAMAUMQIAAEwRIwAAwBQxAgAATBEjAADAFDECAABM/R9H4Jw+xYZnCgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def uniforme_discrete(card):\n",
    "    plt.figure()\n",
    "    x = range(0, card +1 )\n",
    "    y = [0]\n",
    "    for i in range(1, card +1):\n",
    "        y.append(i/card)\n",
    "    plt.step(x, y)\n",
    "    \n",
    "uniforme_discrete(6)\n",
    "uniforme_discrete(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "892f6ef4-f53d-4d76-b4c6-5a2372c20925",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f799a2ebdc0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def uniforme(a, b, card):\n",
    "    x = np.linspace(a, b, card)\n",
    "    y = np.zeros(card)\n",
    "    for i in range(card):\n",
    "        y[i] = i/card\n",
    "    addANumber = lambda A: np.array([A for i in range(100)])\n",
    "    x = np.concatenate((np.linspace(-1, 0, 100), x, np.linspace(1, 2, 100)))\n",
    "    y = np.concatenate((addANumber(0), y, addANumber(1)))\n",
    "    return x, y\n",
    "    \n",
    "Ux, Uy = uniforme(0, 1, 200)\n",
    "plt.plot(Ux, Uy, label='Loi uniforme')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7139a7c7-a974-4a30-aa76-c1d298924972",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f799a218d00>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def traceFctRepEmpirique01(ens):\n",
    "    card = len(ens)\n",
    "    x = np.concatenate((np.array([min(ens)-1]), ens, np.array([max(ens)+1])))\n",
    "    x.sort()\n",
    "    y = [0]\n",
    "    for i in range(card + 1):\n",
    "        y.append(i/card)\n",
    "    plt.step(x, y, label=f\"Card={card}\")\n",
    "    plt.legend()\n",
    "    plt.grid()\n",
    "    \n",
    "traceFctRepEmpirique01([0, 1, 9, 6, 3, 12, 2, 9])\n",
    "plt.figure()\n",
    "for n in [5, 15, 100]:\n",
    "    traceFctRepEmpirique01(np.random.rand(n))\n",
    "x,y = uniforme(0, 1, 200)\n",
    "plt.plot(x,y, label='Fonction limite')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67f8652e-08ae-475e-b83b-5a3b1b457d78",
   "metadata": {},
   "source": [
    "Fonction de répartition: 1 - exp(-lambda * x)\n",
    "\n",
    "Fonction inverse : -1/lambda * ln(1-U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "a05d8992-dc36-4880-9018-33447c5de924",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 3.0)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def inverse_F(U, lam):\n",
    "    return -1/lam * np.log(1-U)\n",
    "\n",
    "def simuExp():\n",
    "    return inverse_F(np.random.rand(), lam)\n",
    "\n",
    "def exponentielle(m):\n",
    "    return 1-np.exp(-lam * x)\n",
    "\n",
    "lam = 1\n",
    "m = math.ceil(-np.log(0.05)/lam)\n",
    "\n",
    "for n in [100, 1000, 5000]:\n",
    "    traceFctRepEmpirique01([simuExp() for _ in range(n)])\n",
    "    \n",
    "x = np.linspace(0, m, 200)\n",
    "plt.plot(x, exponentielle(x), label='Fonction de répartion')\n",
    "plt.legend()\n",
    "plt.gca().set_xlim(0, m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "3958036d-a251-4e77-ba1d-438d0c0be2a8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-12.706204736174696, 12.706204736174696)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def arct(X):\n",
    "    return np.arctan(X)/np.pi + 1/2\n",
    "\n",
    "def inverse_arct(X):\n",
    "    return np.tan(np.pi * (X - 1/2))\n",
    "\n",
    "def simuCauchy():\n",
    "    return inverse_arct(np.random.rand())\n",
    "\n",
    "m = np.tan(np.pi * 0.475)\n",
    "\n",
    "for n in [50, 100, 1000]:\n",
    "    traceFctRepEmpirique01([simuCauchy() for _ in range(n)])\n",
    "\n",
    "x = np.linspace(-m, m, 200)\n",
    "plt.plot(x, arct(x), label='Fonction de répartion')\n",
    "plt.legend()\n",
    "plt.gca().set_xlim(-m, m)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}