12. Suppose that X, the interarrival time between two customers entering a certain postoffice, satisfies P (X > t) = et + et, t

12. Suppose that X, the interarrival time between two customers entering a certain postoffice, satisfies P (X > t) = αe−λt + βe−µt, 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.