Terry is a small business entrepreneur and owns 6 buildings forbusiness use. The probability distribution below describes expectedproperty losses for the group of 6 buildings. Assume that theproperty exposures are independent of each other.

Losses$                                                        Probability of Loss

$10,000                                                          0.20

$20,000                                                          0.10

$50,000                                                          0.06

$100,000                                                        0.03

$500,000                                                        0.01

Now suppose Terry joins a risk sharing arrangement with othersmall business owners and now a total of 18 buildings are in therisk sharing pool. Assume that the property losses for theadditional buildings follow the same probability distribution asthat given for Terry’s buildings and losses are independent.

a. Find the average or expected loss of this larger group ofbuildings in a given year.

b. Calculate the standard deviation of the distribution.

c. Find the Coefficient of Variation

d. What happens to variance or risk for Terry after the sharingarrangement is in place?

e. What would you expect to happen to variance or risk if thepool was extremely large? Why?

f. What is Terry’s actuarially fair premium now? What hashappened to his risk premium now?