Exercise 2. A stock market trader buys 50 shares of stock A and 100 shares of stock B. Let X and Y be the price changes to A and B, respectively, over certain period of time. Assume that the joint PMF pX, Y (x, y) is uniform over the set of integers satisfying −1 ≤ x ≤ 3, −1 ≤ y − x ≤ 1. (this means that the joint PMF is constant over the integers in this set) (a) Find the joint PMF pX, Y (x, y), the marginal PMFs pX(x) and pY (y). (b) Find E[X] and E[Y ]. (c) Determine the trader’s profit.