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..