5-1. Given the following bivariate probability distribution, determine the sets of marginal probabilities for the X and Y random variables. Find:

Y 0 1 2 3 X

0 3

87 3

87 5

87 5

87 1

4 87 6

87 8

87 10 87 2

7 87 9

87 12 87 15 87

(a) F(1, 2)

(b) P(1 ≤ Y ≤ 3)

(c) The marginal probability distributions of X and Y

(d) P(X = 1|Y = 1)

(e) P(Y = 2|X = 0)

(f) The conditional distribution of X given Y = 3

(g) The conditional distribution of Y given X = 2. Are X and Y independent?