1. The ports of Long Beach (POLB) and Los Angeles (POLA) are two of the bussiest ports on the West Coast. Denote the number of cargo ships being cleared at POLB and POLA every day by X and Y, respectively. The following table shows the joint pmf of X and Y. '9 May) 1 3 4 1 0.04 0.16 0.13 x 2 0.2 0.11 0.02 3 0.09 0.07 0.18 (a) Find the marginal distribution, expected value, and standard deviation of X at any given day. (b) Find the probabilities P(X + Y S 5) and P(X + Y 5 5 | X g 2). (c) Compute P(X g 2, Y S 3). Using this probability (and two other probabilities) check whether X and Y are independent. (d) Compute the covariance between X and Y. (e) The POLA management plans to transition to a 24/7 workshift, which will double the number of cargo that can be cleared any day. How will the results from part (a) and (d) change