Provide an easy to follow answer.

(i) The following multiple state model has been suggested as a representation of deaths and style retirements between the ages of 59 and 60. There are no other decrements and the forces of decrement # and u are constant. Let py denote the probability that a life is in state / at age x +t given that it was in state / at age x. d = dead a = active r = retired (a) State the assumptions underlying the above model. (b) Show that - pod =e (toll for 59 Exx+$60. (c) Suppose that you make the following observations in respect of n identical and statistically independent lives: v = time spent in the active state d = number of deaths r = number of retirements Assuming that lives are only observed to the earlier of death or retirement, show that the likelihood for # and u given these observations is: Lu,u) = e-lately (d) Give formulae (without proof) for: the maximum likelihood estimator of the parameter u the asymptotic expected value of the estimator an estimated standard error of the estimator. [16] (ii) Suppose that you learn that retirements can only take place on a birthday, so that r is the number of retirements at exact age 60. In addition to v , d and r you also observe: m = number of lives attaining exact age 60, where man . Suppose that any life attaining exact age 60 will retire with probability k , where 0