5-6. Let the bivariate probability mass function of the discrete random variables X and Y be given as f (X,Y) = -X+Y 36 , X = 1, 2, 3 and Y = 1, 2, 3;

0 elsewhere.

Find:

(a) P(X = 2, Y ≤ 2)

(b) F(2, 2)

(c) The marginal probability mass functions of X and Y

(d) The marginal probability distribution of X

(e) The conditional probability distribution of Y given X = 1 Are the X and Y random variables independent?