Answer the following questions clearly explaining your answers.

During a period of length 7 years, you observe a total of N lives between the ages of x and x +1. You do not necessarily observe each life for the entire year of age. The total time spent under observation by the / lives is V . d deaths are observed. (i) State the assumptions underlying the Poisson model for d, given that the force of mortality between the ages of x and x + 1 is a constant, !. [2] (ii) Show that the maximum likelihood estimator of u is D/V, under the assumptions in (i) above. [2] (iii) Show that the maximum likelihood estimator has: (a) an expected value of u (b) a variance of w/V . [2] [Total 6]The force of interest at time / is given by: 0.01 +0.01 05/