A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self- service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. y p(x, y) 1 2 .10 .04 .02 1 .08 .20 .06 .06 .14 .30 (a) Compute the marginal probability of X and Y (b) What is the probability that there is exactly one hose being used on the self-service island at a particular time? (c) Compute the expected values of X and Y

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