A service station has both self service and full service

Last updated: 4/19/2023

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 X 1 a Given that X 1 determine the conditional pmf of Y i e Pyx 011 Py x 1 1 Py x 211 Round your answers to four decimal places 0 1 2 PY X Y 1 y 0 1 2 Py x 12 y 2 1 0 03 0 01 0 06 0 20 0 08 0 0 10 0 06 0 14 0 32 0 06 X X 0 06 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 1 2 0 20 X X 0 14 0 08 X X 0 32 RACTICE ANOTHER 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 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 1 2 0