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) 0 0 0.10 0.04 0.02 1 0.08 0.20 0.06 2 0.05 0.14 0.31 (a) Given that X-1, determine the conditional pmf of Y-i.e., pYlx(011), pnx(111), 1x(211). (Round your answers to four decimal places.) 0 Pnxl1) (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 Pynx12) (c) Use the result of part (b) to calculate the conditional probability P(Y 1 | X = 2). (Round your answer to four decimal places.) (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 decimal places.) (Round your answers to four 0 Pxix12)

Explanation / Answer

for above joint probability distirbution:

a)

by dividing each cell in row x=1 by its total below is condition distirbution:

b) likewise:

c)

P(y<=1|X=2) =0.1+0.28 =0.38

d)

y x 0 1 2 Total 0 0.1000 0.0400 0.0200 0.1600 1 0.0800 0.2000 0.0600 0.3400 2 0.0500 0.1400 0.3100 0.5000 Total 0.2300 0.3800 0.3900 1.0000

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