from matplotlib.pyplot import *
from random import *
from math import log,exp
def Expo(a):
    return -1/a*log(1-random())
def tirages(n,a):
    L=[]
    for i in range(n):
        L.append(Expo(a))
    return L
def graphe(n,a):
    L=tirages(n,a)
    maxL=int(max(L))
    hist(L , bins = 100, range=(0,maxL), normed = True)
    x = [float(i)/100 for i in range(100*maxL)]
    f = [a*exp(-a*t) for t in x]
    plot(x,f)
graphe(10000,0.5)