The future lifetimes tx and ty are independent and each has

The future lifetimes Tx and Ty are independent, and each has the distribution de?ned by the p.d.f.

f(y) = (0.02(10 - t), 0 < t < 100, elsewhere

(a) Determine the survival function and force of mortality of this distribution.

(b) Determine the actuarial present value of a payment of 1, 000 at the moment of death of (x) providing that (y) is still alive , using δ = .04.

(c) Determine the actuarial present value of a payment of 1, 000 at the moment of death of (y) if predeceased by (x), using δ = .04.

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