Mathematics, 19.03.2021 18:20 kinz5550
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
x 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).
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) Use the result of part (b) to calculate the conditional probability 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?
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