A company scheme provides the following benefits for its employees in the event of their death: Class of worker Number Benefit Probability of death 1 2 3 4 (a) (b) 100 200 100 200 5,000 10,000 5,000 10,000 0.001 0.001 0.015 0.015 Assuming independence, find the mean and variance of the total claims per annum. Find the relative security loading, if premiums are to be 95% sure to exceed claims.