feat: PBS2 mer. 11 mars 2026 17:53:57 CETHEADmain

4 files changed, 117 insertions, 0 deletions

diff --git a/PBS2/.jupyter_ystore.db b/PBS2/.jupyter_ystore.db
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+++ b/PBS2/.jupyter_ystore.db
diff --git a/PBS2/Cours1.md b/PBS2/Cours1.md
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+def ensembliste de l'évènement impossible
+
+**Probabilité conditionnelle** : $$P[E | A]$$ (E sachant A) = Probabilité de l'évènement E sachant que A est sur
+
+**Fonction de répartition** : Probabilités cumulées $$F_X(t) = P[X \leq t]$$
+
+Différence espérance - moyenne
+Espérance : Résultat espéré sur un grand nombre d'expériences = théorique
+Moyenne : résultat moyen sur les expériences = pratique
+
+**Variance** Espérance des écarts à l'espérance pour $X$
diff --git a/PBS2/TD1.md b/PBS2/TD1.md
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+# Exercice 1
+$$
+n>=2, n \in \mathbb{N}, X_1, X_2,\dots, X_n des VAR mutuellement indépendantes de loi \mathcal{B}(p),
+p \in ]0;1[
+$$
+
+## 1
+$$
+S_n = \sum_{i=1}^{N}X_i
+$$
+$S_n$ suit une loi Binomiale
+
+## 2
+$S_n \approx \mathcal{P}(1)$
+
+## 3
diff --git a/PBS2/Untitled.ipynb b/PBS2/Untitled.ipynb
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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "9b604e23-db98-4106-b0c0-74e72625dfd5",
+   "metadata": {},
+   "source": [
+    "# Exercice 1\n",
+    "$n>=2, n \\in \\mathbb{N}, X_1, X_2,\\dots, X_n$ des VAR mutuellement indépendantes de loi $\\mathcal{B}(p)$, $p \\in ]0;1[$\n",
+    "\n",
+    "## 1\n",
+    "$$\n",
+    "S_n = \\sum_{i=1}^{N}X_i\n",
+    "$$\n",
+    "$S_n$ suit une loi Binomiale\n",
+    "\n",
+    "## 2\n",
+    "$S_n \\approx \\mathcal{P}(1)$\n",
+    "\n",
+    "## 3\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "da4ff45a-49e3-4b51-904d-2cdd31a1b2ff",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[0.7 0.  0.9 0.4 0.8 0.5 0.2 1.  0.7 0.3 0.1 0.3 0.  0.  0.  0.1 0.  0.3\n",
+      " 0.8 0.2 0.1 0.9 0.2 0.5 0.3 0.3 0.8 0.4 0.5 1.  0.4 0.3 0.2 0.9 0.4 0.6\n",
+      " 0.7 0.7 1.  0.1 0.5 0.4 0.  0.7 0.  0.2 0.3 0.  0.1 0.6]\n",
+      "18\n"
+     ]
+    }
+   ],
+   "source": [
+    "import random\n",
+    "import numpy as np\n",
+    "\n",
+    "n = 50 #int(input(\"nombre essais\"))\n",
+    "p = 0.3 #float(input(\"proba succès générique\"))\n",
+    "def binom(n, p):\n",
+    "    U = np.zeros(n)\n",
+    "    for k in range(n):\n",
+    "        U[k] = random.randint(0,10) / 10\n",
+    "    S = sum([U[i] < p for i in range(n)])\n",
+    "    return S"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "f89c7bbe-ad75-4c23-a504-4b9c36df0895",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def poiss(l):\n",
+    "    n = 1e6\n",
+    "    p = l/n\n",
+    "    X = Binom(n,p)\n",
+    "    return X"
+   ]
+  }
+ ],
+ "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": "3.13.11"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}