Two fair dice are thrown. Let X denote the largest face that appears and Y denote the smallest face that appears.

(a) Find the joint probability distribution.

(b) Find the conditional distribution f (x|y) and show that E(X|Y = y) = 42−y2 13−2y

, y =

1, 2, … , 6.

Then use this result to find E(X).

(c) Show that E(Y|X = x) = x2 2x−1

, x = 1, 2, … , 6 and use this result to find E(Y).

(d) Explain why E(X + Y) = 7.