A failure time t has a pdf of f t 12 - t72 for 0 le t 12, Ask an Expert

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A failure time T has a p.d.f. of f (t) = (12 - t)/72 for 0 ≤ t 12. An annuity contract provides for continuous payments at the annual rate of 1, which stop at failure, or at time 6 if earlier. The interest rate is 0. Let Y denote the present value of the benefits.

(a) Express Y as a function of T.

(b) Calculate E(Y) and Var(Y).

(c) The single premium charged for this contract is the expected value plus 20%. What is the probability that the premium will cover the benefits?

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