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.

1) Find the joint mass function of X and Y

2) Find the conditional mass function of X given that Y=i. Do it for i=1,2,3,4,5.

3) Are X and Y independent? Why?