37. Calculate EIn and VarIn using a conditioning argument in the following cases: (a) Let In denote...

37. Calculate E½In and Var½In using a conditioning argument in the following cases:

(a) Let In denote the random variable which equals the present value of a life insurance payment at the end of the year of death, but where a payment is made only if death occurs in the first n years. This is an ‘‘n-year term insurance’’ contract.

(b) Let In denote the random variable that equals the present value of a life insurance payment at the end of the year of death if death occurs in the first n years, or a payment of $1 at time t ¼ n if the individual survives the n years. This is an ‘‘n-year endowment’’ contract.