A stochastic variable X can have values x = 1 and x = 3. A stochastic variable Y can have values y = 2 and y = 4. Denote the joint probability density Pxy(x,y)=-13-24 Pij6(xi)6(y-j). Compute the covariance of X and Y for the following two cases:

(a) P1,2 = P1,4 P32 = P3,4 = and

(b) P1,2 = P3,4 = 0 and P1,4 P3,2 . For each case, decide if X and Y are independent.