1. ## Probability problem

Hey !
I have this exercise to do :
Let Z be a standard normal random variable and let Y1=Z and Y2=Z^2.

a) What are E(Y1) and E(Y2)?

b) What is E(Y1Y2)?

c) What is Cov(Y1, Y2)?

d) Notice that P(Y2>1|Y1>1)=1. Are Y1 and Y2 independent?

I found E(Y1)=0 and E(Y2)=1/2
But then because it is not given that Y1 and Y2 are independent I can't find E(Y1Y2)

Thanks for any help..

2. E[Z] - You're kidding, right? Maybe zero (0)?

E[Z^2] - (E[Z])^2 = Var(Z)

Consider E((Y1+Y2)^2)

4. $E(Y_1Y_2)=E(Z^3)=0$ by symmetry