Answer Happy

4. (20 marks) A life insurance company covers 16,000 lives for 1-year term life insurance in amount shown in Table 1. The probability of a claim for each of the 16,000 lives, assumed to be mutually independent, is Benefit Amount Number Covered 1 8,000 2 3,500 3 2,500 5 1,500 10 500 Table 1: 1-Year Term Life Insurance for 16,000 Lives. 0.010. The company wants to set a retention limit R. For each life, the retention limit is the amount below which this company will retain the insurance and above which it will purchase reinsurance coverage from another company. The reinsurance cost is 0.020 per unit. Assume 3 <R<5. Calculate the following: (a) The mean and variance of the retained claim S in terms of R. (b) The reinsurance amount A and the reinsurance cost c in terms of R. (c) Using a normal distribution approximation to calculate the probability in terms of R) that the total cost (S+c) will exceed 600. (d) Find R that minimizes the probability given in Part (c).