Group 1. A fire insurance company covers 200 contracts against fire damage up to an amount stated in the contract. The numbers of contracts at the different contract amounts are given below. Class k Contract amount in thousand Number of contracts 1 2 3 4 5 2 3 4 5 6 80 40 20 30 30 Probability of occurrence of the claim 0.01 0.02 0.03 0.04 0.05 Assume that the conditional distribution of the claim size, given that a claim has occurred, follows a truncated exponential distribution over the interval from 0 to the contract amount and the parameter of the exponential density is 1. Let S be the amount aggregate claims in a 1-year period. 1. Calculate the mean and variance of S. 2. Use a normal approximation to calculate the safety loading premiums to be requested so the company can collect an amount equal to the 100th percentile of the distribution of total claims for a 0.70, 0.75, 0.80, 0.85, 0.90, 0.95. ld