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.

An attorney came to work on a saturday. when he signed in, he was advised by the morning security guard employed by the building management that he must be out of the building by 5 p. m., when it closes. however, he stayed past 5 p. m. to complete a brief that had to be filed on monday morning. at 5: 15 p. m., the afternoon security guard set the locks on all the doors of the building and left. because she was in a hurry, she did not check the sign-in sheet to make sure that everyone had signed out, contrary to mandatory procedures. when the attorney tried to exit 15 minutes later, he discovered that the doors were all locked and could not be opened from the inside. he used his cell phone to call for , and a supervisor from the building arrived and let him out shortly thereafter. if the attorney sues the building management for false imprisonment, is he likely to win?