RACTICE ANOTHER 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) 0 1 2 0 0.10 0.03 0.01 X 1 0.06 0.20 0.08 2 0.06 0.14 0.32 (a) Given that X = 1, determine the conditional pmf of Y-i.e., Py|x(011), P|x(111), Py|x(211). (Round your answers to four decimal places.) 0 1 2 .PYX(1) 0.06 X 0.20 X 0.08 X (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 y PX|X(12) 0.06 0.14 1 2 X 0.32 X (c) Use the result of part (b) to calculate the conditional probability P(Y 1 | X = 2). (Round your answer to four decimal places.) P(Y 1 X = 2) = 0.3846 I (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 0 1 2