Aservice 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. yp(x, y) 0 1 2x 0 0.10 0.03 0.01 1 0.08 0.20 0.06 2 0.05 0.14 0.33 (a) given that x = 1, determine the conditional pmf of y�i. e., py|x(0|1), py|x(1|1), py|x(2|1). (round your answers to four decimal places.) y 0 1 2py|x(y|1) (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.) y 0 1 2py|x(y|2) (c) use the result of part (b) to calculate the conditional probabilityp(y ? 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 0 1 2px|y(x|2)