Refer to the attachment

5 An actuarial student is using Empirical Bayes Credibility Theory Model 2 to calculate credibility premiums for a group of insurers. The student has analysed the data for six different insurers, using 10 years of past data for each insurer and has obtained the following figures: 6 10 EXP = 1, 498 p* = 18.24 The estimated values of Elm(@)], E[s (@)] and var[m(@)] based on the data from the six insurers are 4.00, 62.8 and 42.1, respectively. The student has just received the following information relating to a seventh insurer (Insurer I), and he wishes to update the estimates of Elm(O)], E[s (@)] and var[m(@)] using the claims data for Insurer I given in the below: Year, j 1 2 3 5 6 7 9 10 Aggregate claim 100 85 90 102 109 106 128 150 131 amount, 132 Risk volume, 22 24 26 20 25 30 29 35 40 36 (1) Calculate the updated estimates for E[m(0)], E[s (@)] and var[m(@)], and hence calculate the credibility premium for Insurer I for the coming year, given that Insurer I is expected to have a risk volume figure for the coming year of 38. [18] (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: VKj = 986 and ) Pkj = 327 1=1 j=1 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 | (per unit of risk volume). [2] [Total 20]A company makes annual sales of $3,000,000 and incurs costs of E2,700,000, both of which are spread evenly over the year. Assume that: a tax bill of f150,000 is due to be paid in April the company begins the year with a cash balance of f10,000 a large customer has informed the company that a f100,000 payment expected in January will only be paid in February. Draw up a table to help the company forecast its cash resources over the months of January to April inclusive, and comment on the company's circumstances. [5]