The frequency distribution shown in the next table depicts the property and marine losses incurred by a large oil company over the last 2 years. This distribution can be used by the company to predict future losses and to help determine an appropriate level of insurance coverage. In analyzing the losses within an interval of the distribution, for simplification, analysts may treat the interval as a uniform probability distribution (Research Review, Summer 1998). In the insurance business, intervals like these are often called layers.

a. Use a uniform distribution to model the loss amount in layer 2. Graph the distribution. Calculate and interpret its mean and variance.
b. Repeat part a for layer 6.
c. If a loss occurs in layer 2, what is the probability that it exceeds $10,000? That it is under $25,000?
d. If a layer-6 loss occurs, what is the probability that it is between $750,000 and $1,000,000? That it exceeds $900,000? That it is exactly $900,000?

Property and Marine Losses (millions of $) Layer Frequency 668 38 0.00-0.01 0.01-0.05 0.05-0.10 0.10-0.25 0.25-0.50 0.50-1.00 1.00-2.50