IUT/2A/Maths/tp/projet/projet.ipynb

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    "# Exercice 1\n",
    "1) Combien y a t'il de dominos dans un jeu classique ?  \n",
    "Un jeu de dominos classique est composé de 28 pièces dont chaque moitié comporte un certain nombre de petits points allant de 0 à 6, sans doublons, ce qui donne 7 * 4 = 28 pièces.\n",
    "\n",
    "2) Pourquoi est-il possible que le jeu s'arrête sans avoir posé tous les dominos ?  \n",
    "Il est possible que le jeu s'arrete avant d'avoir posé tout les dominos car chaque moitié comporte un certain nombre de petits points allant de 0 à 6. Si les combinaisons de dominos disponibles dans la pioche ne sont pas compatibles avec les extrémités de la chaîne déjà construite, le jeu peut se terminer sans avoir posé tous les dominos. Cela dépend de la chance et de l'ordre dans lequel les dominos sont tirés.\n",
    "\n",
    "3) Pourquoi X et Y sont des variables aléatoires ?  \n",
    "X et Y sont des variables aléatoires car leur valeur dépend du hasard et des choix effectués tout au long du jeu. La variable aléatoire X représente le nombre de dominos posés dans la chaîne, et elle dépend du nombre de dominos tirés et de la possibilité de les placer à chaque étape. De même, la variable aléatoire Y représente le nombre de points restants dans la pioche, ce qui dépend également de la manière dont les dominos sont tirés et placés. En raison de la nature aléatoire du jeu, X et Y prennent des valeurs différentes à chaque partie, d'où leur caractère aléatoire. Pour comprendre leur comportement, il est nécessaire d'étudier leur distribution de probabilité."
   ]
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    "- Quelle structure de données pour représenter la pioche de dominos restants ?\n",
    "    - La structure nécéssaire est une file car on insere en queue mais on supprime en tete\n",
    "- Quelle structure de données pour représenter la chaîne de dominos déjà construite? (Sachant qu'il suffit de considérer l'information pertinente pour le déroulement du jeu.)\n",
    "    - Une liste car c'est une fassons simple de stocker les dominos mis en place sur le tapis\n",
    "- Comment savoir si le jeu est \u001c",
    "fini ?\n",
    "    - si on ne peut plus inserer en tete ou en queue les dominos de la pioche.\n",
    "- Est-il éventuellement utile d'écrire certaines sous-fonctions, afin de clarifier le code ?  \n",
    "    - Ca peut être plus simple à comprendre le code, notamment pour le comptage de Y."
   ]
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   "id": "060f3b6e-ed57-4ecc-9338-f2491f54bd74",
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   "source": [
    "exemple de file en python :"
   ]
  },
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   "execution_count": 10,
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "[2, 3]\n"
     ]
    }
   ],
   "source": [
    "queue = []                 # la file est vide\n",
    "\n",
    "queue.append(1)            # la file contient [1]\n",
    "queue.append(2)            # la file contient [1, 2]\n",
    "queue.append(3)            # la file contient [1, 2, 3]\n",
    "\n",
    "result = queue.pop(0)      # la file contient [2, 3]\n",
    "\n",
    "print(result)\n",
    "print(queue)"
   ]
  },
  {
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   "id": "5fabca55-4ebf-4499-b652-86844be439e5",
   "metadata": {},
   "source": [
    "**Initialisation et affichage de la pioche**"
   ]
  },
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     "text": [
      "[1, 1]\n",
      "[1, 2]\n",
      "[1, 3]\n",
      "[1, 4]\n",
      "[1, 5]\n",
      "[1, 6]\n",
      "[2, 2]\n",
      "[2, 3]\n",
      "[2, 4]\n",
      "[2, 5]\n",
      "[2, 6]\n",
      "[3, 3]\n",
      "[3, 4]\n",
      "[3, 5]\n",
      "[3, 6]\n",
      "[4, 4]\n",
      "[4, 5]\n",
      "[4, 6]\n",
      "[5, 5]\n",
      "[5, 6]\n",
      "[6, 6]\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "# initialisation de la pioche contenant 28 pièces\n",
    "pioche = [[i, j] for i in range(1,7) for j in range(i, 7)]\n",
    "\n",
    "# Exemple d'utilisation : affichez la file de dominos\n",
    "for domino in pioche:\n",
    "    print(domino)"
   ]
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    "def comptePoints(P):\n",
    "    # Initialise un compteur pour les points\n",
    "    nb = 0\n",
    "    \n",
    "    # Parcours tous les dominos de la liste\n",
    "    for domino in P:\n",
    "        # Ajoute les points des deux moitiés du domino\n",
    "        nb += sum(domino)\n",
    "    \n",
    "    return nb"
   ]
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     "text": [
      "X = 13, Y = 70\n"
     ]
    }
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   "source": [
    "# Fonction pour simuler une partie du jeu de dominos\n",
    "def une_chaine_domino():\n",
    "    # Liste représentant les dominos sur le jeu\n",
    "    tapis = []\n",
    "\n",
    "    #initialisation d'une variable pour compter le nombre de pioche dans la pioche\n",
    "    cpt = 0\n",
    "    \n",
    "    # Liste représentant la pioche de dominos restants\n",
    "    pioche = [(i, j) for i in range(1, 7) for j in range(i, 7)]\n",
    "\n",
    "    # Tant que la pioche n'est pas vide et qu'on peut poser des dominos\n",
    "    while pioche:\n",
    "        domino = random.choice(pioche)  # Tirer un domino au hasard\n",
    "        pioche.remove(domino)  # Retirer le domino de la pioche\n",
    "\n",
    "        if not tapis:  # Si c'est le premier domino, ajoutez-le directement\n",
    "            tapis.append(domino)\n",
    "        else:\n",
    "            # Vérifiez si le domino peut être placé à l'une des extrémités de la chaîne\n",
    "            if domino[0] == tapis[0][0] or domino[1] == tapis[0][0]:\n",
    "                tapis.insert(0, domino)  # Placez-le au début de la chaîne\n",
    "                cpt = 0;\n",
    "            elif domino[0] == tapis[0][1] or domino[1] == tapis[0][1]: # On regarde le second argument du premier couple du tapis\n",
    "                tapis.append(domino)  # Placez-le à la fin de la chaîne\n",
    "                cpt = 0;\n",
    "            else:\n",
    "                pioche.append(domino)\n",
    "                cpt = cpt + 1;\n",
    "                if(cpt > len(pioche)):\n",
    "                    break  # Si après un tour entier de la pioche est éfféctué sans pour voir placer un domino\n",
    "\n",
    "    # Valeur de X : nombre de dominos posés dans la chaîne\n",
    "    X = len(tapis)\n",
    "\n",
    "    # Valeur de Y : nombre de points restants dans la pioche\n",
    "    Y = comptePoints(pioche)\n",
    "\n",
    "    return X, Y\n",
    "\n",
    "# Utilisation de la fonction\n",
    "X, Y = une_chaine_domino()\n",
    "print(f\"X = {X}, Y = {Y}\")"
   ]
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   "source": [
    "# Exercice 3 (Analyse probabiliste).  \n",
    "Simulez un grand nombre de réalisations du jeu (au moins 10000).  \n",
    "Puis, à l'aide des méthodes déjà vues en cours et en TP :"
   ]
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     "text": [
      "Moyenne de X : 14.9434\n",
      "Moyenne de Y : 47.56\n"
     ]
    }
   ],
   "source": [
    "# Nombre de réalisations du jeu\n",
    "nombre_de_realisations = 10000\n",
    "\n",
    "# Liste pour stocker les résultats des n réalisations\n",
    "resultats = []\n",
    "\n",
    "# Simulez le jeu un grand nombre de fois et stockez les résultats\n",
    "for _ in range(nombre_de_realisations):\n",
    "    X, Y = une_chaine_domino()\n",
    "    resultats.append((X, Y))\n",
    "\n",
    "# Vous pouvez maintenant analyser les résultats pour obtenir des statistiques\n",
    "# Par exemple, vous pouvez calculer la moyenne et l'écart-type pour X et Y.\n",
    "moyenne_X = sum(X for X, Y in resultats) / nombre_de_realisations\n",
    "moyenne_Y = sum(Y for X, Y in resultats) / nombre_de_realisations\n",
    "\n",
    "# Affichez les résultats statistiques\n",
    "print(f\"Moyenne de X : {moyenne_X}\")\n",
    "print(f\"Moyenne de Y : {moyenne_Y}\")"
   ]
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    "1. Estimer et représenter la loi de probabilité de la variable X.\n",
    "2. Calculer et tracer la fonction de répartition de X.\n",
    "3. Estimer l'espérance de X.\n",
    "4. Estimer la variance de X.\n",
    "5. Mêmes questions pour la variable Y .\n",
    "6. Estimer la probabilité de succès au jeu, c'est-à-dire, la probabilité de parvenir à placer tous\n",
    "les dominos dans la chaine.\n",
    "7. Estimer le nombre médian de points restants dans la pioche."
   ]
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   "source": [
    "Pour répondre à ces questions, vous pouvez utiliser les résultats de votre simulation du jeu de dominos pour estimer les propriétés des variables aléatoires X et Y. Voici comment vous pouvez procéder pour chaque question :\n",
    "\n",
    "1. Estimer et représenter la loi de probabilité de la variable X :\n",
    "   Pour estimer la loi de probabilité de X, comptez le nombre de fois où chaque valeur de X apparaît dans vos résultats et divisez-le par le nombre total de réalisations. Vous pouvez ensuite représenter cette distribution de probabilité sous forme d'histogramme.\n",
    "\n",
    "2. Calculer et tracer la fonction de répartition de X :\n",
    "   Pour calculer la fonction de répartition (CDF) de X, triez d'abord les valeurs de X dans l'ordre croissant, puis calculez la proportion de réalisations avec des valeurs de X inférieures ou égales à chaque valeur donnée.\n",
    "\n",
    "3. Estimer l'espérance de X :\n",
    "   L'espérance de X (la moyenne) peut être estimée en calculant la moyenne des valeurs de X dans vos résultats.\n",
    "\n",
    "4. Estimer la variance de X :\n",
    "   Pour estimer la variance de X, calculez la variance des valeurs de X dans vos résultats. Vous pouvez également estimer l'écart-type en prenant la racine carrée de la variance.\n",
    "\n",
    "5. Mêmes questions pour la variable Y :\n",
    "   Utilisez la même approche que pour X pour estimer et représenter la loi de probabilité de Y, calculer et tracer la fonction de répartition de Y, estimer l'espérance de Y et la variance de Y.\n",
    "\n",
    "6. Estimer la probabilité de succès au jeu :\n",
    "   La probabilité de succès au jeu est le rapport du nombre de réalisations où X est égal au nombre total de dominos dans un jeu (28) par le nombre total de réalisations.\n",
    "\n",
    "7. Estimer le nombre médian de points restants dans la pioche :\n",
    "   Pour estimer le nombre médian de points restants dans la pioche, triez d'abord les valeurs de Y dans l'ordre croissant et trouvez la médiane."
   ]
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    "# Exercice 4 (Covariance et corrélation) :\n",
    "\n",
    "1. Pour effectuer 200 réalisations du jeu, vous pouvez utiliser votre fonction `une_chaine_domino` pour obtenir les valeurs de X et Y. Ensuite, vous pouvez représenter ces valeurs sous la forme d'un nuage de points en utilisant la bibliothèque Matplotlib. Voici comment vous pouvez le faire :\n",
    "\n",
    "   ```python\n",
    "   import matplotlib.pyplot as plt\n",
    "\n",
    "   # Effectuer 200 réalisations du jeu\n",
    "   nombre_de_realisations = 200\n",
    "   resultats = [une_chaine_domino() for _ in range(nombre_de_realisations)]\n",
    "\n",
    "   # Extraire les valeurs de X et Y dans des listes distinctes\n",
    "   X_valeurs = [X for X, Y in resultats]\n",
    "   Y_valeurs = [Y for X, Y in resultats]\n",
    "\n",
    "   # Créer un nuage de points\n",
    "   plt.figure(figsize=(8, 6))\n",
    "   plt.scatter(X_valeurs, Y_valeurs, alpha=0.5)\n",
    "   plt.title('Nuage de points de X et Y')\n",
    "   plt.xlabel('Valeurs de X')\n",
    "   plt.ylabel('Valeurs de Y')\n",
    "   plt.grid(True)\n",
    "   plt.show()\n",
    "   ```\n",
    "\n",
    "   L'interprétation du nuage de points peut vous permettre de visualiser s'il existe une relation entre les valeurs de X et Y.\n",
    "\n",
    "2. Le nombre Z = X * Y est une variable aléatoire car il dépend des variables aléatoires X et Y. Tant que X et Y sont des variables aléatoires, toute combinaison linéaire de celles-ci est également une variable aléatoire.\n",
    "\n",
    "3. Pour estimer l'espérance de X, Y et Z, vous pouvez calculer la moyenne des valeurs observées dans vos réalisations. Pour vérifier l'indépendance de X et Y, vous pouvez calculer la covariance de X et Y. Si la covariance est proche de zéro, cela suggère que X et Y sont indépendants. Pour le calcul de la covariance, vous pouvez utiliser la fonction `np.cov` de NumPy.\n",
    "\n",
    "   ```python\n",
    "   esperance_X = np.mean(X_valeurs)\n",
    "   esperance_Y = np.mean(Y_valeurs)\n",
    "\n",
    "   # Calcul de Z = X * Y pour chaque réalisation\n",
    "   Z_valeurs = [X * Y for X, Y in resultats]\n",
    "   esperance_Z = np.mean(Z_valeurs)\n",
    "\n",
    "   # Calcul de la covariance entre X et Y\n",
    "   covariance_XY = np.cov(X_valeurs, Y_valeurs)[0, 1]\n",
    "\n",
    "   # Vérification d'indépendance\n",
    "   independants = abs(covariance_XY) < 1e-10\n",
    "   ```\n",
    "\n",
    "4. Pour estimer la covariance des variables X et Y, vous pouvez utiliser la valeur `covariance_XY` calculée précédemment. Pour le coefficient de corrélation, vous pouvez diviser la covariance par le produit des écarts-types de X et Y. Le coefficient de corrélation mesure la force et la direction de la relation linéaire entre les variables. Un coefficient de corrélation proche de 1 ou -1 indique une forte corrélation, tandis qu'un coefficient proche de 0 indique une faible corrélation.\n",
    "\n",
    "   ```python\n",
    "   ecart_type_X = np.std(X_valeurs)\n",
    "   ecart_type_Y = np.std(Y_valeurs)\n",
    "   coefficient_correlation = covariance_XY / (ecart_type_X * ecart_type_Y)\n",
    "   ```\n",
    "\n",
    "   Vous pouvez commenter sur la signification du coefficient de corrélation : s'il est proche de 1 ou -1, cela indique une forte corrélation linéaire entre X et Y, tandis qu'un coefficient proche de 0 indique une faible corrélation.\n",
    "\n",
    "Ces étapes vous permettront d'explorer la relation entre les variables X, Y et Z, d'estimer leurs espérances, de vérifier l'indépendance de X et Y, et de calculer la covariance et le coefficient de corrélation entre X et Y."
   ]
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    "1) Effectuer 200 réalisations du jeu et représenter les valeurs correspondantes de X et Y sous la forme d'un nuage de points (avec un point (x,y) pour chaque réalisation de X et Y observée). Interprétez le résultat."
   ]
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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# ... (votre code pour obtenir X_valeurs et Y_valeurs)\n",
    "# Effectuer 200 réalisations du jeu\n",
    "nombre_de_realisations = 200\n",
    "resultats = [une_chaine_domino() for _ in range(nombre_de_realisations)]\n",
    "\n",
    "# Extraire les valeurs de X et Y dans des listes distinctes\n",
    "X_valeurs = [X for X, Y in resultats]\n",
    "Y_valeurs = [Y for X, Y in resultats]\n",
    "\n",
    "# Ajuster une régression linéaire aux points\n",
    "coefficients = np.polyfit(X_valeurs, Y_valeurs, 1)\n",
    "slope, intercept = coefficients\n",
    "\n",
    "# Créer un nuage de points\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.scatter(X_valeurs, Y_valeurs, alpha=0.5)\n",
    "\n",
    "# Tracer la droite de régression linéaire\n",
    "x_range = np.linspace(min(X_valeurs), max(X_valeurs), 100)\n",
    "y_fit = slope * x_range + intercept\n",
    "plt.plot(x_range, y_fit, color='red', label=f'Régression Linéaire')\n",
    "\n",
    "plt.title('Nuage de points de X et Y avec Régression Linéaire et Médiane de Y')\n",
    "plt.xlabel('Valeurs de X')\n",
    "plt.ylabel('Valeurs de Y')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e625af4f-7df2-4f31-8f55-d7b9e2b96d78",
   "metadata": {},
   "source": [
    "2) On définit le nombre Z = X × Y comme le produit entre X et Y . Expliquer pourquoi Z est une variable aléatoire."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78884a6a-548d-4f24-af2c-e0c2220d4e53",
   "metadata": {},
   "source": [
    "Z est une variable aléatoire car c'est un produit de variables àléatoires"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "fa92c9dc-cd8f-45b4-8b33-8e98c333c419",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "esperance de X :  14.61\n",
      "esperance de Y :  50.45\n",
      "esperance de Z :  675.645\n",
      "covariance de X et Y :  -61.73819095477388\n",
      "X et Y indépendants ? :  False\n"
     ]
    }
   ],
   "source": [
    "esperance_X = np.mean(X_valeurs)\n",
    "esperance_Y = np.mean(Y_valeurs)\n",
    "\n",
    "# Calcul de Z = X * Y pour chaque réalisation\n",
    "Z_valeurs = [X * Y for X, Y in resultats]\n",
    "esperance_Z = np.mean(Z_valeurs)\n",
    "\n",
    "# Calcul de la covariance entre X et Y\n",
    "covariance_XY = np.cov(X_valeurs, Y_valeurs)[0, 1]\n",
    "\n",
    "# Vérification d'indépendance\n",
    "independants = abs(covariance_XY) < 1e-10\n",
    "\n",
    "print(\"esperance de X : \", esperance_X)\n",
    "print(\"esperance de Y : \", esperance_Y)\n",
    "\n",
    "print(\"esperance de Z : \", esperance_Z)\n",
    "\n",
    "print(\"covariance de X et Y : \", covariance_XY)\n",
    "\n",
    "print(\"X et Y indépendants ? : \", independants)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "7fec6ae6-4157-4742-90fc-9f6e569c8446",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ecart tyope de X :  2.8527004749885676\n",
      "ecart tyope de Y :  22.241121824224606\n",
      "coefficient de correlation :  -0.9730631729407484\n"
     ]
    }
   ],
   "source": [
    "ecart_type_X = np.std(X_valeurs)\n",
    "ecart_type_Y = np.std(Y_valeurs)\n",
    "coefficient_correlation = covariance_XY / (ecart_type_X * ecart_type_Y)\n",
    "\n",
    "print(\"ecart tyope de X : \", ecart_type_X)\n",
    "print(\"ecart tyope de Y : \", ecart_type_Y)\n",
    "print(\"coefficient de correlation : \", coefficient_correlation)"
   ]
  }
 ],
 "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": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}