fact that the odd moments of a standard normal random variable are all zero, that is E(X)= E(X^3)=E(X^5)=0c) Show that cov(X,Y)=0 and thus corr(x,y)=0

Hi, I am not exactly how to figure this out. Could someone show me detailed steps?This exercise provides an example of a pair of random variables x and y for which the conditional mean of y given x depends on x but corr (x, y)=0. In other words, y and x are uncorrelated but not independent. Let x and z be two independently distributed standard normal random variables, and let y=x^2 + za) show that E(y given x) = x^2b) show that E(XY)=0 (Hint: use the fact that the odd moments of a standard normal random variable are all zero, that is E(X)= E(X^3)=E(X^5)=0c) Show that cov(X,Y)=0 and thus corr(x,y)=0