from math import *
import matplotlib.pyplot as plt
import random
import scipy

def VoirCentralLimite(p,n):
    '''approximation continue de la loi discrète de Bernoulli'''
    x = 0
    sigma = sqrt(p*(1-p)/n)
    Lx, Ly = [],[]
    Gx, Gy = [],[]
    for i in range(n+1):
        Lx.append(x+1/(2*n))
        Gx.append(x)
        Ly.append(n*scipy.misc.comb(n, i)*p**i * (1-p)**(n-i))
        Gy.append((1/sqrt(2*pi*sigma**2))*exp(-((x-p)**2/(2*(sigma**2)))))
        x = x + 1/n
  Lx.append(x)
        Ly.append(n*scipy.misc.comb(n, i)*p**i * (1-p)**(n-i))
    plt.plot(Lx,Ly,'b-')   #pour la loi de Bernoulli
    plt.plot(Gx, Gy, 'r-') #pour le contour gaussien