1. The problem statement, all variables and given/known data Let X,Y be two independent normal N(0,1) and N(0,2) variables, and Z=XY. Suppose that E(X^4)=3 a) Compute Var(X), Var(Y), Var(Z), Cov(X,Y), Cov(Y,Z), Var(X+Y), Var(X+Z) b) By computing E[(X^2)(Z^2)], prove that X,Z are not independent. 2. Relevant equations Var(X)=E(X^2)-E(X)^2 Cov(X,Y)=E[(X-E(X))(Y-E(Y))] 3. The attempt at a solution I know that Var(X)=1, Var(Y)=2, Cov(X,Y)=0. The others I'm not sure about. I found that Var(Z)=E[(X^2)(Y^2)] but I'm not sure if E[(X^2)(Y^2)]=E[X^2]E[Y^2]? I'm having similar problems with the other parts.