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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. P(x, y) 0 2 0.10 0, 05 0.02 X 0.07 0.20 0.07 0.05 0.14 0.30 (a) Given that X = 1, determine the conditional pmf of Y-i.e., Pyx(0|1), Pyx(1|1), Pyx(2|1). (Round your answers to four decimal places.) 2 (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? (Round your answers to four decimal places.) 0 Pyx( 12 ) (c) Use the result of part (b) to calculate the conditional probability P(Y's 1 | X = 2). (Round your answer to four decimal places.) P(Y $ 1| X = 2) = (d) 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? (Round your answers to four decimal places.) X 2 Pay(x12) OLIOLO ? a 8:06 P 3/2/20