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An actuarial student is using Empirical Bayes Credibility Theory Model 2 to calculate credibility premiums for a group of insurers. He has analysed the data for six different insurers, using 10 years of past data for each insurer. He has obtained the following figures: 10 JSP; = 1, 498 P* =18.24 i=l j=1 E[me)] = 4.00 var m(9)] = 42.1 E s' (@) = 62.8 He has just received the following information relating to a 71 insurer (Insurer D), and he wishes to update his estimates using the past ten years of claims data for Insurer I given in the table below: Year i 1 2 3 4 5 Aggregate 100 85 90 102 109 claims Volume 22 24 26 20 25 Year i 6 7 9 10 Aggregate 106 128 132 150 131 claims Volume 30 29 35 40 36 (i) Calculate his updated estimates for Em(9)]. E s?(@) and var[m(e)], and hence find the credibility premium for Insurer I for the coming year, given that Insurer I is expected to have a volume figure for the coming year of 38. [20] (ii) The student also needs a credibility estimate for Insurer K, one of the six insurers included in the original analysis. He knows that. for Insurer K. [Yx; =986 and PK; =327. Explain whether the credibility premium for Insurer K (based on the full analysis of the seven insurers) will be greater or less than the corresponding figure for Insurer I (per unit of risk volume), and give reasons for your answer. 13] [Total 23]