from math import sqrt
print('Hello world!')
Y=[2**k for k in range(1,11)]
print("Y=",Y)
P=[]
for i in range(1,11):
    if i==1 :
        P.append(0.15)
    else :
        if i==6 :
            P.append(0.05)
        else :
            P.append(0.1)
print("P=",P)
def esperanceY() :
    X=0
    for i in range(0,10) :
        X=X+Y[i]*P[i]
    return X
print("espérance =",esperanceY())
def varianceY() :
    X=0
    for i in range(0,10):
        X=X+P[i]*(Y[i]-esperanceY())**2
    return X
print("variance =",varianceY())
def ecarttypeY() :
    X=sqrt(varianceY())
    return X
print("écart type =",round(ecarttypeY(),2))