2BCPST1
TD6 - Corrig´
e
"""
2BCPST1 - TD 6
Variables aleatoires discr`
etes I
Lois discretes usuelles : loi binomiale et loi hypergeometrique
"""
plt.plot(x,y)
plt.show()
# EXERCICE 3
from random import shuffle
from random import randint
N = 100
p = 0.45
# EXERCICE 1
from scipy.misc import comb
def loi_binomiale(k,n,p):
if k in range(0,n+1):
return comb(n,k) * p**k * (1-p)**(n-k)
else:
return 0
L = [1] * 45 + [0] * 55
shuffle(L)
def tir():
T = []
for i in range(10):
k = randint(0,N-1)
T.append(L[k])
return T
def loi_hypergeometrique(k,N,n,P):
if k in range(0,n+1):
return comb(N*P,k) * comb(N*(1-P),n-k) / comb(N,n)
else:
return 0
def frequence(m = 1000):
Freq = [0] * 11
for i in range(m):
T = tir()
compteur = 0
for x in T:
if x==1:
compteur += 1
Freq[compteur] += 1/m
return Freq
# EXERCICE 2
import matplotlib.pyplot as plt
import numpy as np
n = 10
p = 0.4
x = np.arange(0,n+1)
loi_binomiale_v = np.vectorize(loi_binomiale)
y = loi_binomiale_v(x,n,p)
plt.figure(1)
plt.clf()
plt.vlines(x,0,y,lw=2)
plt.plot(x,y,’o’)
plt.show()
y = frequence()
plt.figure(2)
plt.clf()
plt.vlines(x,0,y,lw=2)
plt.plot(x,y,’o’)
z = loi_binomiale_v(x,10,p)
plt.plot(x,z)
plt.title("Tir avec remise et loi binomiale")
plt.show()
loi_hypergeometrique_v = np.vectorize(loi_hypergeometrique)
for N in range(20,50,10):
y = loi_hypergeometrique_v(x,N,n,p)
1
2BCPST1
TD6 - Corrig´
e
# EXERCICE 4
from random import sample
def tir2():
return sample(L,10)
def frequence2(m = 1000):
Freq = [0] * 11
for i in range(m):
T = tir2()
compteur = 0
for x in T:
if x==1:
compteur += 1
Freq[compteur] += 1/m
return Freq
y = frequence2()
plt.figure(3)
plt.clf()
plt.vlines(x,0,y,lw=2)
plt.plot(x,y,’o’)
z = loi_hypergeometrique_v(x,N,10,p)
plt.plot(x,z)
plt.title("Tir sans remise et loi hypergeometrique")
plt.show()
2

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Silver sinter interconnects in diversified

正誤表 1) p. 40 左カラム下から11行目にある kEET の式に使われている