import numpy.random as rd
import matplotlib.pyplot as plt

def date():
    r=rd.randint(0,60)
    return r

def rdv(n):
    L=[]
    for i in range (0,n):
        x=date()
        y=date()
        L.append(abs(x-y))
    return L

# ESPERANCE
L=[k*2*(60-k)/3600 for k in range(1,60)]
print('Espérance :',sum(L))

# SIMULATION

for n in [10,100,1000,10000,100000]:
    L=rdv(n)
    moy=sum(L)/n
    print('n=', n, '-> Moyenne :',moy)

n=100000
Lx=range(0,60)
Ly=[L.count(x)/n for x in Lx]
Lyexact=[1/60]+[2*(60-k)/3600 for k in range(1,60)]
plt.grid()
plt.plot(Lx,Ly)
plt.plot(Lx,Lyexact)
plt.show()