A service station has both seltf-service and tull-service islands. On each islan

Question

A service station has both seltf-service and tull-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 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. (Give answers accurate to 3 decimal places.) p(x,y) 0 0.10 0.10 0.06 0.04 0.21 0.16 0 0.02 0.03 0.28 2 (a) Given that X-1, determine the conditional pmf of Y. py (01), Pyx (11), pYx (211) YP(YIX-1) 0 (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? 0 (c) Use the result of part (b) to calculate the conditional probability P(Y S1iX 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? X p(X|Y= 2) 0

Explanation / Answer

a) dividing each row cell in X=1 ; by row total:

b) similarly as above :

c) P(Y<=1|X=2) =0.294+0.618=0.912

d)

y P(y|X=1) 0 0.625 1 0.25 2 0.125

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