Suppose X and Y are discrete random variables with joint distribution P(X = −1,Y = −1) = 1/9, P(X = −1,Y = 1) = 2/9, P(X = 1,Y = −1) = 4/9 and  P(X = 1, Y = 1) = 2/9.

(i) Calculate the conditional expectations E(X|Y) and E(Y|X);

(ii) Calculate the conditional variances Var(X|Y) and Var(Y|X).