A service station has both self-service and full-service islands. On each island

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)

(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.)

(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.)

(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) =  

(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.)

y

p(x, y)

     0 1 2 x 0     0.10     0.03     0.01   1     0.06     0.20     0.06   2     0.06     0.14     0.34  

Explanation / Answer

A)

B)

C)

D)

y p(x, y) 0 1 2 sum x 0   0.1 0.03 0.01 0.14 1   0.06 0.2 0.06 0.32 2   0.06 0.14 0.34 0.54 total 0.22 0.37 0.41 1

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