Suppose that Kate and Anne enter into a pooling arrangement. Assume that both women have the following loss distributions and that losses are independent.

Loss =

$50,000 with probability 0.01

$1,000 with probability 0.03

$0 with probability 0.96

Write out the possible outcomes and the probability of each outcome for Kate and Anne after they enter into a pooling arrangement. That is, write out the probability distribution for each of the women after they enter into a pooling arrangement.

Possible Outcome

Total Costs

Costs Paid by Each

Probability

2. Calculate the expected loss to each person prior to and subsequent to entering into a pooling arrangement.

3. Calculate the standard deviation of the loss distribution to each person prior to and subsequent to entering into a pooling arrangement. What happens to the standard deviation subsequent to the pooling arrangement?

4. What will happen to the standard deviation if we increase the pool size to 100 million?