From c63d44280373427e7c8bfef55c36be6eea92a703 Mon Sep 17 00:00:00 2001
From: Bertrand Benjamin <benjamin.bertrand@opytex.org>
Date: Wed, 3 May 2023 09:41:41 +0200
Subject: [PATCH] =?UTF-8?q?feat(2nd):=20d=C3=A9but=20du=20chapitre=20le=20?=
 =?UTF-8?q?l'=C3=A9chantillonnage?=
MIME-Version: 1.0
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---
 2nd/18_Echantillonnage/1B_fluctuation.pdf  | Bin 0 -> 20659 bytes
 2nd/18_Echantillonnage/1B_fluctuation.tex  |  37 +++
 2nd/18_Echantillonnage/1E_piece_de.ipynb   | 299 +++++++++++++++++++++
 2nd/18_Echantillonnage/echantillons.py     |  28 ++
 2nd/18_Echantillonnage/exercises.tex       |   7 +
 2nd/18_Echantillonnage/index.rst           |  39 +++
 2nd/18_Echantillonnage/plan_de_travail.tex |  44 +++
 2nd/18_Echantillonnage/solutions.tex       |  28 ++
 8 files changed, 482 insertions(+)
 create mode 100644 2nd/18_Echantillonnage/1B_fluctuation.pdf
 create mode 100644 2nd/18_Echantillonnage/1B_fluctuation.tex
 create mode 100644 2nd/18_Echantillonnage/1E_piece_de.ipynb
 create mode 100644 2nd/18_Echantillonnage/echantillons.py
 create mode 100644 2nd/18_Echantillonnage/exercises.tex
 create mode 100644 2nd/18_Echantillonnage/index.rst
 create mode 100644 2nd/18_Echantillonnage/plan_de_travail.tex
 create mode 100644 2nd/18_Echantillonnage/solutions.tex

diff --git a/2nd/18_Echantillonnage/1B_fluctuation.pdf b/2nd/18_Echantillonnage/1B_fluctuation.pdf
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diff --git a/2nd/18_Echantillonnage/1B_fluctuation.tex b/2nd/18_Echantillonnage/1B_fluctuation.tex
new file mode 100644
index 0000000..c95c31f
--- /dev/null
+++ b/2nd/18_Echantillonnage/1B_fluctuation.tex
@@ -0,0 +1,37 @@
+\documentclass[a4paper,10pt]{article}
+\usepackage{myXsim}
+
+\author{Benjamin Bertrand}
+\title{Echantillonnage - Cours}
+\date{mai 2023}
+
+\pagestyle{empty}
+
+\begin{document}
+
+
+\maketitle
+
+\begin{definition}[Échantillon]
+  Lorsqu’on répète $n$ fois, de façon identique et indépendante, une même expérience aléatoire, on obtient une série de $n$ résultats que l’on appelle échantillon de taille $n$.
+\end{definition}
+
+\begin{definition}[Fluctuation de l'échantillon]
+  Lorsqu’on effectue plusieurs échantillons de même taille, la fréquence d’un caractère observé varie d’un échantillon à l’autre. C’est ce qu’on appelle la \textbf{fluctuation d’échantillonnage}.
+\end{definition}
+
+\begin{propriete}[Estimation d'une probabilité]
+  Dans une population, la proportion p d’individus présentant un certain caractère est inconnue.
+
+  On prélève dans cette population un échantillon aléatoire de taille $n$.
+
+  On note $f$ la fréquence d’apparition du caractère dans l’échantillon.
+
+  La fréquence observée f est appelée une estimation de la proportion $p$.
+\end{propriete}
+
+
+\begin{propriete}[Intervalle de fluctuation]
+
+\end{propriete}
+\end{document}
diff --git a/2nd/18_Echantillonnage/1E_piece_de.ipynb b/2nd/18_Echantillonnage/1E_piece_de.ipynb
new file mode 100644
index 0000000..a80e07d
--- /dev/null
+++ b/2nd/18_Echantillonnage/1E_piece_de.ipynb
@@ -0,0 +1,299 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "f7b010a9",
+   "metadata": {},
+   "source": [
+    "# Echantillonnage\n",
+    "\n",
+    "Dans ce TP, vous allez cherche à savoir si une pièce ou un dé est truqué. C'est à dire s'il donne plus souvent un résultat qu'un autre.\n",
+    "\n",
+    "Si vous le souhaitez, vous pouvez utiliser les outils de programmation pour répondre mais ce n'est pas necessaire."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3574ed56",
+   "metadata": {},
+   "source": [
+    "## Pièce trucquée?\n",
+    "\n",
+    "On importe 3 pièces sous la forme de 3 fonctions Python"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "f8574d02",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from echantillons import piece1, piece2, piece3"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a008af30",
+   "metadata": {},
+   "source": [
+    "Pièce 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "df8982e6",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'pile'"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "piece1()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c858e103",
+   "metadata": {},
+   "source": [
+    "Pièce 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "b98436c2",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'face'"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "piece2()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2f71532e",
+   "metadata": {},
+   "source": [
+    "Pièce 3"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "fa5868a0",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'pile'"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "piece3()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "14eff698",
+   "metadata": {},
+   "source": [
+    "Que pensez-vous? Est-ce que ces pièces sont équilibrées?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b86ec551",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c168731c",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "id": "625a5dfd",
+   "metadata": {},
+   "source": [
+    "## Dé trucqué?\n",
+    "\n",
+    "On importe 3 dés sous la forme de 3 fonctions Python."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "fab62eff",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from echantillons import de1, de2, de3"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9a43f807",
+   "metadata": {},
+   "source": [
+    "Dé 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "582c9ec8",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "6"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "de1()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3cb2d6e7",
+   "metadata": {},
+   "source": [
+    "Dé 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "66b777f8",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "6"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "de2()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a241a4d4",
+   "metadata": {},
+   "source": [
+    "Dé 3"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "05781d0a",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "3"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "de3()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bd4bb96e",
+   "metadata": {},
+   "source": [
+    "Est-ce qu'un dé donne un nombre anormalement élevé de 6? D'un autre nombre? Lequel semble bien équilibré?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c391b26c",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "81d2f6fa",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "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": "3.10.10"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/2nd/18_Echantillonnage/echantillons.py b/2nd/18_Echantillonnage/echantillons.py
new file mode 100644
index 0000000..d3b71e3
--- /dev/null
+++ b/2nd/18_Echantillonnage/echantillons.py
@@ -0,0 +1,28 @@
+from random import random
+
+def piece_builder(p):
+    def piece():
+        r = random()
+        if r < p:
+            return "pile"
+        return "face"
+
+    return piece
+
+piece1 = piece_builder(0.5)
+piece2 = piece_builder(0.4)
+piece3 = piece_builder(0.2)
+
+def de_builder(steps):
+    assert sorted(steps) == steps
+    assert steps[-1] == 1
+    def de():
+        r = random()
+        for i in range(6):
+            if r < steps[i]:
+                return i+1
+    return de
+
+de1 = de_builder([(i+1)*1/6 for i in range(6)])
+de2 = de_builder([0.1, 0.2, 0.3, 0.4, 0.5, 1])
+de3 = de_builder([0.01, 0.3, 0.4, 0.6, 0.8, 1])
diff --git a/2nd/18_Echantillonnage/exercises.tex b/2nd/18_Echantillonnage/exercises.tex
new file mode 100644
index 0000000..9f0a5bd
--- /dev/null
+++ b/2nd/18_Echantillonnage/exercises.tex
@@ -0,0 +1,7 @@
+\begin{exercise}[subtitle={<++>}, step={1}, origin={<++>}, topics={ Echantillonnage }, tags={ Probabilité, Statistiques, Python, Tableur }]
+    <++>
+\end{exercise}
+
+\begin{solution}
+    <++>
+\end{solution}
diff --git a/2nd/18_Echantillonnage/index.rst b/2nd/18_Echantillonnage/index.rst
new file mode 100644
index 0000000..162f73e
--- /dev/null
+++ b/2nd/18_Echantillonnage/index.rst
@@ -0,0 +1,39 @@
+Echantillonnage
+###############
+
+:date: 2023-05-03
+:modified: 2023-05-03
+:authors: Benjamin Bertrand
+:tags: Probabilité, Statistiques, Python, Tableur
+:category: 2nd
+:summary: Étude de la fluctuation d'un échantillon.
+
+
+Éléments du programme
+=====================
+
+
+Progression
+===========
+
+Étape 1: Construction d'échantillon
+-----------------------------------
+
+Activité avec Capytale, les élèves ont 3 pièces à eux de déterminer une méthode pour savoir si elle est équilibrée. Ils auront ensuite trois dés. Ils devront rédiger leur méthode sur le cahier de groupe.
+
+Le but est de faire émerger les notions suivantes:
+
+- d'échantillon
+- de tendance de la fréquence à se stabliliser sur la probabilité.
+
+Bilan: echantillon, stabilisation de la fréquence et intervalle de fluctuation.
+
+Étape 2: Stabilisation de la fréquence
+--------------------------------------
+
+Si le temps le permet: activité tableur pour observer cette stabilisation.
+
+Étape 2: Intervalle de fluctuation
+----------------------------------
+
+Exercices techniques d'utilisation de l'intervalle de fluctuation.
diff --git a/2nd/18_Echantillonnage/plan_de_travail.tex b/2nd/18_Echantillonnage/plan_de_travail.tex
new file mode 100644
index 0000000..fd97ba8
--- /dev/null
+++ b/2nd/18_Echantillonnage/plan_de_travail.tex
@@ -0,0 +1,44 @@
+\documentclass[a4paper,12pt]{article}
+\usepackage{myXsim}
+
+\author{Benjamin Bertrand}
+\title{Echantillonnage - Plan de travail}
+\tribe{2nd}
+\date{mai 2023}
+
+\pagestyle{empty}
+
+\DeclareExerciseCollection{banque}
+\xsimsetup{
+}
+
+
+\begin{document}
+\maketitle
+
+% Résumé
+
+\bigskip
+
+Savoir-faire de la séquence
+\begin{itemize}
+    \item
+\end{itemize}
+
+\bigskip
+
+Ordre des étapes à respecter
+
+
+\section{}
+
+\listsectionexercises
+
+
+\pagebreak
+
+\input{exercises.tex}
+\printcollection{banque}
+
+
+\end{document}
diff --git a/2nd/18_Echantillonnage/solutions.tex b/2nd/18_Echantillonnage/solutions.tex
new file mode 100644
index 0000000..3606691
--- /dev/null
+++ b/2nd/18_Echantillonnage/solutions.tex
@@ -0,0 +1,28 @@
+\documentclass[a4paper,10pt]{article}
+\usepackage{myXsim}
+
+\usetikzlibrary{shapes.geometric}
+
+\author{Benjamin Bertrand}
+\title{Echantillonnage - Solutions}
+\tribe{2nd}
+\date{mai 2023}
+
+\DeclareExerciseCollection{banque}
+\xsimsetup{
+    exercise/print=false,
+    solution/print=true,
+}
+
+\pagestyle{empty}
+
+
+\begin{document}
+
+\maketitle
+
+\input{exercises.tex}
+%\printcollection{banque}
+%\printsolutions{exercises}
+
+\end{document}