Question: 14. Suppose that X, the interarrival time between two customers entering a certain postoffice, satisfies where + = 1, 0,

14. Suppose that X, the interarrival time between two customers entering a certain postoffice, satisfies

P(X >t)=ae + Bet -Xt t 0,

where α + β = 1, α ≥ 0, β ≥ 0, λ > 0, μ > 0. Calculate the expected value of X.
Hint: For a fast calculation, use Remark 6.4.

P(X >t)=ae + Bet -Xt t 0,

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