please solve while showing all the steps

(i) State the principle of correspondence as it relates to mortality investigations. Two small countries conduct population censuses on an annual basis. Country A records its population on 1 February every year based on an age definition of age last birthday. Country B records its population on every 1 August using a definition of age nearest birthday. Each country records deaths as they happen based on age next birthday. Below are some data from the last few years. Country: A Age last Population Population Population birthday ! February 2011 1 February 2012 ] February 2013 44 382,000 394,000 401,000 45 374,000 351,000 385,000 46 354,000 372,000 375,000 Country B Age nearest Population Population Population birthday I August 201 1 I August 2012 I August 2013 44 382,000 394,000 401,000 45 374,000 381,000 385,000 AG 354,000 372,000 375,000 In the combined lands of Countries A and B in the calendar year 2012 there were 4,800 deaths of those aged 46 next birthday and 4,500 deaths of those aged 45 next birthday. The two countries decide to form an economic union. after which it will be mandatory to offer the same rates for life insurance to residents of each country. (ii) Estimate the death rate at age 45 years last birthday for the two countries combined. 16] (iii) Explain the exact age to which your estimate relates. (1] [Total 8]An insurer's portfolio consists of three independent policies. Each policy can give rise to at most one claim per month, which occurs with probability 0 independently from month to month. The prior distribution of 0 is beta with parameters o = 2 and 5 = 4. A wial of 9 claims are observed on this portfolio over a 12 month period. (1) Derive the posterior distribution of 0. [2] (ii) Derive the Bayesian estimate of 0 under all or nothing loss. (4] [Total G] Individual claim amounts on a particular insurance policy can take the values 100, 150 or 200 There is at most one claim in a year. Annual premiums are 60. The insurer must choose between three reinsurance arrangements: A no reinsurance individual excess of loss with retention 150 for a premium of 10 C proportional reinsurance of 25% for a premium of 20 (i) Complete the loss table for the insurer. [4] Reinsurance Claims A B C 0 100 150 200 (ii) Determine whether any of the reinsurance arrangements is dominated from the viewpoint of the insurer. (2] (iii) Determine the minimax solution for the insurer. [Total 71