5-39. Suppose (X,Y) is a bivariate random variable and X and Y are discrete

(or continuous). If X and Y are independent random variables, which of the following is a valid equality?

(a) E XY

 = E(X) · E 1Y



(b) E XY = E(X)

E(Y)

Verify your choice via the following random experiment. Vessel A contains three identical chips numbered 1, 2, 3; vessel B also contains three identical chips numbered 1, 2, 3. A chip is drawn at random from each vessel simultaneously. Construct the sample space S (there are nine simple events in S) by plotting the outcome obtained from vessel A (the random variable X) on the horizontal axis and the outcome obtained from vessel B (the random variable Y) on the vertical axis. Construct the discrete probability distribution for X, Y, 1/Y, and X/Y. Find E(X),E(Y),E(1/Y), and E(X/Y).