4. (40 points) A local supermarket has three checkout counters. Two customers arrive at the counters at different times when the counters are serving no other customers. Each customer chooses a counter at random, independently of the other. Let X denote the number of customers who choose counter 1 and Y, the number who select counter 2. a) Write the joint PMF ofX and Y. b) Determine the marginal PMF of X and marginal PMF of Y. c) Determine the expectation of marginal PMF of X and the expectation of marginal PMF of Y. d) Let Z = X + 2Y, determine the expectation of Z