Choose a number X at random from the set of numbers {1, 2, 3, 4, 5}. Now

Question:

Choose a number X at random from the set of numbers {1, 2, 3, 4, 5}. Now choose a number at random from the subset no larger than X, that is, from {1, . . . ,X}. Call this second number Y.
(a) Find the joint mass function of X and Y.
(b) Find the conditional mass function of X given that Y = i. Do it for i = 1, 2, 3, 4, 5.
(c) Are X and Y independent? Why?