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z*;qj!d=hI1Og(P@p$1!~gC6AcDJA<&DJ9ybd{^|jf>(s|Px(R*!a)HE&1nv#yi%dd z?OlvgtbBOhP|8V|W_)cAtsvI%Xe>C$%JU(~IZtWH#K$RysZ8ezzW_SO6YaozmVAAL zbWpaO7U&PoQ&>o&qzk#f2@a@8$Uk%uUn4p`B}wj!>)@96t=joF+GtXj>%p8-^rZ-ZtcwhU(_>S;JMpY1U9Fd<c&F@$)0CTsSFov S;3;*U#n7h! literal 0 HcmV?d00001 diff --git a/Maths/tp/Stats/tp1/tp.py b/Maths/tp/Stats/tp1/tp.py new file mode 100644 index 0000000..9250285 --- /dev/null +++ b/Maths/tp/Stats/tp1/tp.py @@ -0,0 +1,213 @@ +import numpy as np +import matplotlib.pyplot as plt + +# dans python +import random +#générer un nombre aléatoire +random_number = random.random() +print(random_number) +#générer un entier aléatoire +random_int= random.randint(10,20) # doit etre compris entre 10 et 19 et le troisieme pour le nb qu'on veut +print(random_int) +# dans numpy +#générer un tableau de nombres aléatoires : example +random_tab= np.random.random([2,10]) +print(random_tab.shape) + +import random +Echantillon=random.sample(range(1, 50), 6) +print(Echantillon) + +print("-------------------------------------------") + +# Exo 1 + +# Generer une seule ligne de 0 et 1 +Ligne1=np.random.randint(0,2,1) +print(Ligne1) + +print("-------------------------------------------") + +#Genere une seul colone de -1, 1 +Colone1=np.random.randint(0,2,1) +Colone1[Colone1==0]=-1 +print(Colone1) + +print("-------------------------------------------") + +# Générer une matrice (un tableau de deux dimensions) de taille de réels positifs et négatifs. +Matrice1=np.random.randint(0,2,[10,10]) +Matrice1[Matrice1==0]=-1 +print(Matrice1) + +print("-------------------------------------------") + +# générer deux matrices : A aléatoire de taille [n,m] et B de la même taille que A mais ne contient que 0 et 1. Multiplier A et B (élément par élément) et afficher le résultat +A=np.random.randint(0,2,[10,10]) +A[A==0]=-1 +print(A) +B=np.random.randint(0,2,[10,10]) +print(B) +C=A*B +print(C) + + +# A l'aide de linspace, générer un tableau ax de 100 ponits començant à 0 et finissant à 1. Générer deux lignes aléatoires x et y de la même taille que ax. Dans une figure, afficher les points qui ont pour abscisse x et ordonnée y. +import numpy as np +import matplotlib.pyplot as plt +ax=np.linspace(0,1,100) +x=np.random.random(100) +y=np.random.random(100) +plt.plot(x,y,'o') +plt.show() + + +#Choix aléatoire avec python +from random import choice + +Villes_européenens = ["Berlin", "Porto", "Madrid", "Amsterdam", "London", "Paris", "Rome", "Paris", "Barcelone", "Bruxelles", "Budapest", "Bucarest", "Lisbonne", "Stockholm", "Prague", "Vienne", "Dublin", "Milan", "Copenhague"] + +print('Cette année direction : ',choice(Villes_européenens)) + +print("-------------------------------------------") + +# Exo 2 + +def de(N): + return np.random.randint(1,7,N) + +T = 100000 +y = 6 +tirage=de(T) + +x= len(tirage[tirage==y]) +print("Taux d'apparition du nombre 6 sur le de : ", x/T * 100 ,"%") + +print(len(tirage[tirage==y])) + +print("-------------------------------------------") + +# Exo 3 + + +colone=np.random.randint(0,100,[10,1]) +print(colone) +# 1 +print("mean, moyenne : ", np.mean(colone)) +print("median, mediane : ", np.median(colone)) + +print("-------------------------------------------") +# 2 +print("moyenne : ", np.mean(colone)) +print("variance : ", np.var(colone)) +print("ecart type : ", np.std(colone)) + +print("-------------------------------------------") +# 3 +matrice=np.random.rand(4,3) +print(matrice) +# print("moyenne : ", np.mean(matrice[10,1])) +# print("variance : ", np.var(matrice[10,1])) +# print("ecart type : ", np.std(matrice[10,1])) +print("moyenne : ", np.mean(matrice)) +print("variance : ", np.var(matrice)) +print("ecart type : ", np.std(matrice)) + +print("-------------------------------------------") + +# Générer une matrice aléatoire de taille [4, 3] +matrice = np.random.rand(4, 3) + +# Calculer la moyenne, la médiane et l'écart-type ligne par ligne +moyennes = np.mean(matrice, axis=1) +medianes = np.median(matrice, axis=1) +ecarts_types = np.std(matrice, axis=1) + +# Afficher les résultats +print("Matrice aléatoire:\n", matrice) +print("Moyennes par ligne:", moyennes) +print("Médianes par ligne:", medianes) +print("Écart-types par ligne:", ecarts_types) + +print("-------------------------------------------") + + +# Calculer la moyenne, la médiane et l'écart-type colonne par colonne +moyennes = np.mean(matrice, axis=0) +medianes = np.median(matrice, axis=0) +ecarts_types = np.std(matrice, axis=0) + +# Afficher les résultats +print("Matrice aléatoire : ", matrice) +print("Moyennes par colonne : ", moyennes) +print("Médianes par colonne : ", medianes) +print("Écart-types par colonne : ", ecarts_types) + +# Exo 4 + +# 1 +def lancer_de(): + return np.random.randint(1, 6) + +# 2 +IN = [10, 100, 1000] + +for n in IN: + nb_3 = 0 + for i in range(n): + if lancer_de() == 3: + nb_3 += 1 + freq_3 = nb_3 / n + print("Fréquence de 3 après", n, "lancers:", freq_3) + +# 4 +N = [10, 100, 1000] + +for n in N: + nb_k = 0 + for i in range(n): + if lancer_de() < 4: + nb_k += 1 + freq_k = nb_k / n + print("Fréquence de k < 4 après", n, "lancers:", freq_k) + +# 5 +import matplotlib.pyplot as plt + +probas = [1/6] * 6 # Probabilités théoriques + +plt.bar(range(1, 7), probas) +plt.xlabel("Face du dé") +plt.ylabel("Probabilité") +plt.title("Probabilités d'obtenir chaque face du dé") +plt.show() + +# 6 +N = [10, 100, 1000] + +for n in N: + freq_faces = [0] * 6 + for i in range(n): + face = lancer_de() + freq_faces[face-1] += 1 + freq_faces = [f / n for f in freq_faces] + print("Fréquences de chaque face après", n, "lancers:", freq_faces) + + +# 7 +probas = [1/6] * 6 # Probabilités théoriques +cumul_theo = [sum(probas[:i+1]) for i in range(6)] # Fonction de répartition théorique + +plt.plot(range(1, 7), cumul_theo) +plt.xlabel("Face du dé") +plt.ylabel("Probabilité") +plt.title("Fonction de répartition théorique") +plt.show() + + +# Exo 5 +# 3 +line = np.random.randint(0, 11, size=N-1000) +print(line) + +# 4