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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. Le

Question

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) 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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Mathematics
3 years
2021-07-25T12:33:34+00:00
2021-07-25T12:33:34+00:00 1 Answers
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## Answers ( )

Answer:(a): The conditional pmf of Y when X = 1(b): The conditional pmf of Y when X = 2(c): From (b) calculate P(Y<=1 | X =2)(d): The conditional pmf of X when Y = 2Step-by-step explanation:GivenThe above table

Solving (a): The conditional pmf of Y when X = 1This implies that we calculateSo, we have:Reading the data from the given table, the equation becomesUsing the format of the above formula for the rest, we have:Solving (b): The conditional pmf of Y when X = 2This implies that we calculateSo, we have:Reading the data from the given table, the equation becomesUsing the format of the above formula for the rest, we have:Solving (c): From (b) calculate P(Y<=1 | X =2)To do this, where Y = 0 or 1So, we have:Solving (d): The conditional pmf of X when Y = 2This implies that we calculateSo, we have:Reading the data from the given table, the equation becomesUsing the format of the above formula for the rest, we have: