The picture shows a large rectangle made up of 12 non-overlapping rectangles, with side lengths as shown. Let one be chosen uniformly at random. Let X denote the width (in the horizontal direction) of the chosen rectangle, and let Y denote the height (vertical direction). (a) Find the joint p.m.f. fx,y(x, y) of X and Y. (b) Are X and Y independent? (c) Compute E(X), E(Y) and E(XY)