Find expectation and variance of present value of benefits

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Reference no: EM131001662

1. An insurer charges a single premium of E(X) + 0.1√Var(X) for a contract with present value of benefits equal to X. Use a normal approximation.

(a) How many contracts must be sold so that the probability is 95% that premiums cover benefits?

(b) What is the probability that premiums cover benefits if 225 contracts are sold?

2. A failure time has a hazard rate of μ(t) = 2/20 - t.

A contract provides for a benefit of 1 at time 10 provided that failure occurs before time 10 (so, for example, if failure occurs at time 6, the benefit is not paid until 4 years later). You are given that v(10) = 0.6. Find the expectation and variance of the present value of the benefits.

Reference no: EM131001662

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