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An actuary wishes to analyse the amounts paid by a group of insurers on their respective portfolios of commercial property insurance policies using the models of Empirical Bayes Credibility Theory. The actuary obtains the following information about the amounts of claim payments made and the number of policies sold for each of three different insurers. The data obtained are as follows. Year 1 Year 2 Year 3 Year 4 Insurer A (14.2m $15.8m (21.7m (19.0m 163 189 252 199 Insurer B 658.Gm $63.1m (31.0m $64.2m 4.435 4.761 5.576 4,581 Insurer C {123m (132m f161m f133m 16, 184 17.443 20.102 18.000 (1) Analyse the data using EBCT Model 1, and calculate the expected total claim payment to be made by Insurer B in the coming year. [6] (Hi) Analyse the data using EBCT Model 2, and again calculate the expected payout amount for Insurer B in the coming year, assuming that the expected number of policies sold for the coming year for Insurer B is 4,800. You may use the summary statistics given below. which have been calculated using the formulae and notation given in the Tables, again working in millions of pounds. Subscripts 1, 2 and 3 refer to Insurers A, B and C respectively. [8] ERANY; - X1 =0014667 ER,(X; - X)' = 5105461 ER;(X2; - X2)' =0.006103 EPzi (X2, - X) =0336408 EP,(X3, - X;)' - 0.003979 EP, (X;) - X)2 -0.292541 (iii) Comment on your results. [2]