Lel annual equivalence principle premiums are

Question

1. For a certain failure time T, an insurance contract pays benefits at the end of the year of failure. You are given that s_T(9) = 0.8, s_T(10) = 0.7 E(₁₀L) = 70, Var(₁₀L) = 1000. The amount payable at time 10 for failure between time 9 and time 10 is 100. The interest rate is a constant 20 %. Find Var(₉L).

2. A discrete failure time T has a constant hazard rate of λ(k) = 1/2. There is a constant interest rate of 100%. An insurance contract pays a benefit of 1 unit at the end of the year of failure. Level annual equivalence principle premiums are payable prior to failure.S how that for any nonnegative integer r, Var(_rL) = 1/15.