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A certain product has a failure time of T. The approximating discrete random variable T has a constant hazard function 𝜆(k) = 0.3. (In other words, there is a 30% chance that the product will fail each year, given that it was still working at the beginning of the year.) An insurer agrees to pay 100 at the end of the year of failure should the product fail within 2 years. In return it collects a premium of 40 now and a second premium of 20 at time 1, if failure did not occur in the first year. The interest rate is 25%.

(a) Find E(L), Var(L), Var(1L).

(b) Find the probability that, for a given contract, the premiums collected will be sufficient to pay the benefits.

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