1. (10 points) Choose a number X at random from the set of numbers {1, 2, 3, ... . N - 1, N }, and then choose another number Y at random from the subset no larger than X, that is, from {1, 2, 3, ..., X - 1, X ]. (a) Find the joint mass function of X and Y. (b) Are X and Y independent? Why? (c) Determine the expectation E(Y)