Marine losses for an oil company. The frequency distribution shown in the accompanying table depicts the property and marine losses incurred by a large oil company over LO8 a two-year period. In the insurance business, each “loss”

interval is called a layer. Research Review (Summer 1998)

demonstrated that analysts often treat the actual loss value within a layer as a uniform random variable.

Layer Marine Losses

($ thousands)

Relative Frequency 1 0–10 .927 2 10–50 .053 3 50–100 .010 4 100–250 .006 5 250–500 .003 6 500–1,000 .001 7 1,000–2,500 .000 Based on Cozzolino, J. M., and Mikola, P. J. “Applications of the piecewise constant Pareto distribution.” Research Review, Summer 1998, pp. 39–59.

a. Use the uniform distribution to find the mean loss amount in layer 2.

b. Use the uniform distribution to find the mean loss amount in layer 6.

c. If a loss occurs in layer 2, what is the probability that it exceeds $30,000?

d. If a loss occurs in layer 6, what is the probability that it is between $750,000 and $800,000?