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

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

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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.

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