Determine the value of c that makes the function f (x, y) = c(x + y) a joint probability mass function over the nine points with x = 1, 2, 3 and y = 1, 2, 3. Determine the following:

(a) P(X = 1, Y < 4) 

(b) P(X = 1)

(c) P(Y = 2) 

(d) P(X < 2, Y < 2)

(e) E(X), E(Y), V (X), and V (Y )

(f) Marginal probability distribution of X

(g) Conditional probability distribution of Y given that X = 1

(h) Conditional probability distribution of X given that Y = 2

(i) E(Y | X = 1) 

(j) Are X and Y independent?