A whole life insurance with sum insured $2000 is issued to (60). The benefit is payable at the end of the year of death. You are given that Mortality of a newborn life follows the De Moivre model 1 t 100 So(t) { - for 0 100. 0, The annual effective interest rate is i = 0.05. Let Z denote the present value random variable of the benefit. (a) Write down an expression for Z in terms of K60- (b) Calculate E[Z]. 1 (c) Calculate Var(Z). (d) Calculate the probability that the present value of the death benefit will be greater than $500. A whole life insurance with sum insured $2000 is issued to (60). The benefit is payable at the end of the year of death. You are given that Mortality of a newborn life follows the De Moivre model 1 t 100 So(t) { - for 0 100. 0, The annual effective interest rate is i = 0.05. Let Z denote the present value random variable of the benefit. (a) Write down an expression for Z in terms of K60- (b) Calculate E[Z]. 1 (c) Calculate Var(Z). (d) Calculate the probability that the present value of the death benefit will be greater than $500