Suppose your company sells auto insurance with a deductible of d and with no restric- tion on maximal payment. Suppose that the probability of a loss event during a year is 0.01, and the probability that two loss events will occur is negligible. Assume also that the distribution of the loss in the case of a loss event is closely approximated by the exponential distribution with a mean of $2000. There are 7000 policy holders in this group. Use IRM to answer the following questions:

a) What is the expected total loss, E(S)? Express in terms of d.

b) What is the standard deviation of the total loss, SD(S)? Express in terms of d.

c) Let , the probability of company not suffering a loss, to be .9. Express the loading factor in terms of d.

d) Find value of d that will make individual premiums equal to $10.