1. A fire insurance company covers 160 structures against fire damage up to an amount stated in the contact. The numbers of contracts at the different contracts amounts are given below. Contract Amount Number of Contracts 10000 80 20000 35 30000 25 15 5 50000 100000 Assume that for each of the structures, the probability of one claim within a year is 0.04, and the probability of more than one claim is 0. Assume that fires in the structures are mutually independent events. Furthermore, assume that the conditional distribution of the claim size, given that a claim has occurred, is uniformly distributed over the interval form 0 to the contract amount. Let N be the number of claims and let S be the amount of claims in a 1- year period. a. b. C. Calculate the mean and variance of N. Calculate the mean and variance of S. What relative security loading, 0, should be used so the company can collect an amount equal to the 99th percentile of the distribution of total claims? (Use Normal Approximation.)