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

Question

A gas 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 a time. The joint probability mass function of X and Y appears in the following table. (a) What is the probability that both islands have one or more hoses in use? (b) Compute the marginal density function for the self-service (X) island. (c) Given that the self-service island (X) has both pumps in use, what is the expected number of hoses in use for the full-service (Y) island?

Explanation / Answer

a) here probabilty that both have one or more hoses in use =1-0.1-0.04-0.02-0.08-0.06=0.7

b)marginal density of X :

c)E(Y|X=2) =0*(0.06/0.5)+1*(0.14/0.5)+2*(0.3 /0.5)=1.48

x P(x) 0 0.16 1 0.34 2 0.5 total 1

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