Let X, Y and Z be three independent random variables such that E(X)=E(Y)=E(Z)=0 and Var(X)=Var(Y)=Var(Z)=1. Calculate E[(X^2)(Y+5Z)^2]
I know that the answer is 26.
Since all of the expected values of X Y and Z are all the same, I have replaced each expected value of X Y and Z with just E[X]. For example, E[(X^2)(Y^2)] is now (E[X])^4.
Doing this, I'm left with 26E[X^4]
Since the variance of each random variable is one, I know I need to somehow turn E[X^4] into the formula for variance.... Thanks guys