1. A failure time T is uniformly distributed on the interval [0,10]. There is a constant interest rate of zero. An annuity provides for continuous payments at the rate of t at time t, provided that failure has not yet occurred. Find the expectation and variance of the present value of the benefits.
2. A 4-year pure endowment contract on (60) provides for 1000 paid at age 64 if (60) is then alive. Nothing is paid if death occurs before age 64. This is purchased by four level annual premiums of 100. You are given that q60 = 0.1, q61 = 0.2, q62 = 0.25, q63 = 0.30, and the interest rate i is a constant 25%. Write down the exact distribution of 1L. Use this to find 1V.