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. (Give answers accurate to 3 decimal places.) Y p(x, y) 0 1 2x 0 0.10 0.03 0.01 1 0.08 0.20 0.06 2 0.05 0.14 0.33Required:a. Given that X = 1, determine the conditional pmf. b. Given that two hoses are in use at the self-service island, what is the conditional pmf of the number of hoses in use on the full-service island?c. Given that two hoses are in use at the full-service island, what is the conditional pmf of the number in use at the self-service island?