from math import sqrt
X=[1,2,4]
p=[1/6,0.5,1/3]
def esperance(valeurs,probabilites):
  E_X=0
  for i in range(len(valeurs)):
      E_X += probabilites[i]*valeurs[i]
  return E_X
def variance(valeurs,probabilites):
  varX = 0
  E_X=esperance(valeurs,probabilites)
  for i in range(len(valeurs)):   
    varX += probabilites[i]*(valeurs[i]-E_X)**2
  return varX
def ecarttype(valeurs,probabilites):
  return sqrt(variance(valeurs,probabilites))