{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Python – travaux pratiques" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Démarrage\n", "\n", "Il y a plusieurs manières de faire ce TP. \n", "\n", "1. Une possibilité est de télécharger ce notebook (fichier `.ipynb`) en local sur votre ordinateur et de le l'ouvrir avec jupyter notebook. Il vous faut pour cela une installation de python et de jupyter. Cette installation peut se faire très simplement en utilisant la distribution [anaconda](https://www.anaconda.com/distribution/#download-section). \n", "\n", "2. Une autre possibilité si python est installé sur votre ordinateur est de taper les commandes dans la fenêtre de commande (en utilisant `Spyder` ou `IPython`) et de taper vos programmes étant écrits dans votre éditeur de texte préféré. \n", "\n", "3. N'OUBLIEZ PAS DE SAUVEGARDER !!!" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.stats as sps" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from TP_intro_python import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On rappelle que l’aide Python pour une fonction appelée `fun` s’obtient en tapant : `fun?` dans la console." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Prise en main" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "a) On considère n cartes numérotées de 0 à n − 1 et triées par ordre croissant.\n", "- on supprime la première carte,\n", "- on met la suivante à l’autre extrémité du paquet, \n", "- on recommence jusqu’à ce qu’il n’en reste qu’une.\n", "Ecrire un programme qui affiche la liste des cartes supprimées dans l’ordre de leurs suppressions, ainsi que la carte restante.\n", "*Indication : on utilisera une boucle while et la récursivité n’est pas utile.*" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n", "2\n", "4\n", "6\n", "8\n", "1\n", "5\n", "9\n", "7\n", "3\n" ] } ], "source": [ "exo1()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "b) Soit f définie par $f(x) = sin(x)/x$ si $x\\neq 0$ et $f(0) = 1$. Tracer son graphe sur $[−a,a]$ en \n", "rouge, pour $a = 20\\pi$ par exemple. On pourra ajouter un titre et une légende.\n", "Indication : $\\pi$ s’obtient avec `np.pi`, la commande \n", " \n", " plt.plot(x,y,color=\"r\",label=\"ma legende\") \n", " \n", "affiche en rouge la courbe affine par morceaux reliant les points d’abscisses x et d’ordonnées y, la commande\n", "\n", " plt.legend(loc=’best’) \n", " \n", "affiche la légende définie plus haut avec label (en position optimale) et \n", "\n", " plt.title(\"mon titre\") \n", " \n", "donne un titre à la figure." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "exo2()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Loi des Grands Nombres et Théorème Central Limite" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "a) Afin d'illustrer la Loi des Grands Nombres, visualiser la suite $S_n = X_1+···+X_n$ pour $X_i$ une suite de variables aléatoires indépendantes de loi uniforme sur $[−1, 1]$.\n", "\n", "*Indication : pour $x= [x_1,\\dots ,x_n]$, la commande `np.cumsum(x)` retourne le vecteur\n", "$$[x_1, x_1 +x_2, x_1 +x_2 +x_3,\\dots, x_1 +\\dots+x_n]$$ des sommes cumulées des coordonnées de $x$*." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "exo3()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "b) Faire de même avec des variables aléatoires $Y_i$ de loi de Cauchy, c-à-d de densité \n", "$$\\frac 1 \\pi \\frac 1 {1+x^2},$$\n", "qui s'obtiennent par $Y_i = \\tan(\\pi X_i /2)$. La suite $\\frac {\\sum Y_i}{n}$ semble t-elle converger ? Pourquoi ?" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "exo4()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "c) On définit les $X_i$ comme une suite de variables aléatoires indépendantes de loi uniforme sur $[−1, 1]$. Calculer la moyenne $\\mu$ et l'écart-type $\\sigma$ des $X_i$ et vérifier, afin d'illustrer le Théorème Central Limite, que $\\sqrt{n}(S_n − \\mu)/\\sigma$ converge en loi, lorsque $n \\rightarrow\\infty$ vers $\\mathcal{N}(0,1)$ : on se fixera une grande valeur de $n$, on simulera un grand nombre de fois $\\sqrt{n}(S_n − \\mu)/\\sigma$, on en tracera l'histogramme et on le comparera à la densité $\\frac 1 {\\sqrt{2\\pi}\\sigma}e^{-x^2/2}$ de $\\mathcal{N}(0,1)$.\n", " \n", "*Indication : pour $x$ un tableau bidimensionnel de taille $n × p$, `np.sum(x,axis=1)` donne le tableau unidimensionnel de taille $n$ dont les coordonnées sont les sommes des lignes de $x$.*" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "exo5()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Lois continues" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dans ces exercices, on se propose d’identifier la loi d’une variable aléatoire $X$ en traçant l'histogramme d'un grand nombre, $X_1, . . . , X_n$, de réalisations indépendantes de $X$ et en le comparant à la densité supposée de $X$. On rappelle qu'un histogramme d'un échantillon est un diagramme en colonnes exprimant la répartition des valeurs de cet échantillon dans divers intervalles (la renormalisation est faite de façon à ce que l’aire totale vaille 1). \n", "\n", "**Commande Python** :\n", " \n", " plt.hist(mon-echantillon,bins=mon-nombre-de-colonnes,density=1)\n", "\n", "On peut aussi remplacer le paramètre mon-nombre-de-colonnes par le vecteur des abscisses (ordonnées dans l’ordre croissant) des bases des colonnes.\n", "\n", "a) Soient $X$ et $Y$ des variables aléatoires de loi uniforme sur $[−1, 1]$ indépendantes. Illustrer,\n", "via un histogramme, le fait que $X + Y$ a pour densité $\\rho(x) := \\frac 1 4 \\max(2 − |x|, 0)$.\n", "*Indication : utiliser `np.random.rand` pour simuler $X$ et $Y$.*" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "exo6()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "b) Soient $X$ et $Y$ des variables aléatoires de loi exponentielle de paramètre 1, indépendantes. Illustrer, via un histogramme, le fait que $X + Y$ a pour densité $\\mathbf{1}_{x\\geq 0}xe^{−x}$.\n", "\n", "*Indication : utiliser `np.random.exponential`*" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "exo7()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "c) Illustrer la propriété d'absence de mémoire des lois exponentielles : si $X$ suit une loi exponentielle, alors pour tout $t > 0$, la loi de $X − t$ sachant que $X > t$ est la loi de $X$ (c'est la raison pour laquelle on utilise ces lois pour modéliser les durées de vie de composants sans usure).\n", "\n", "*Indication : pour $X$ vecteur de type numpy, $X[X>t]$ est le vecteur $X$ dans lequel on n'a gardé que les coordonnées plus grandes que $t$*." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "exo8()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Lois discrètes\n", "\n", "Un calcul simple montre que lorsque $n$ tend vers l’infini, la loi de binomiale $B(n, \\lambda/n)$ tend vers la loi de Poisson de paramètre $\\lambda$. En pratique, on assimile $B(n, p)$ à la loi de Poisson de paramètre $np$ dès que $np^2 < 0.1$. Illustrer cette proximité de lois en affichant, sur le même graphique, leurs histogrammes en bâtons (sans faire aucune simulation). \n", "\n", "*Indication : les fonctions `sps.poisson.pmf` et `sps.binom.pmf` donnent les probabilités associées aux différentes valeurs que peuvent prendre des variables aléatoires de loi de Poisson et de loi binomiale, la fonction `plt.stem(x, y)` affiche des barres verticales d’abs. x et hauteur y*.\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n * p^2 = 0.025\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "exo9()" ] } ], "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }