5-5. Let a random experiment consist of rolling a fair pair of six-sided dice.

Let the random variable X = |difference of the faces| and let the random variable Y = sum of the faces. Determine the points in S and find:

(a) P(4 ≤ X ≤ 6, 0 ≤ Y ≤ 4)

(b) P(X ≥ 4,Y = 3)

(c) The marginal probability distribution of Y

(d) The conditional probability distribution of X given Y = 3

(e) E(Y) and V(Y)

(f) E(X|Y = 1)
(g) V(Y|X = 4)