Find the marginal probability functions of (a) X and (b) Y for the random variables of Problem 2.54 (c) Determine whether X and Y are independent.

Problem 2.54 reference

The joint probability function of two discrete random variables X and Y is given by f(x,y) =  cxy for x = 1,2,3 and y = 1,2,3 and equals zero otherwise. Find (a) the constant c, (b) P(X = 2, Y = 3), (c) P(1 ≤ X ≤ 2, Y ≤ 2), (d) P(X ≥ 2), (e) P(Y < 2), (f) P(X = 1), (g) P(Y = 3).