Pooling Assignment (Make sure you show your work!)

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 =	$40,000 with probability 0.02
	$5,000 with probability 0.06
	$ 0 with probability 0.92

1. 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. Hint: the sum of the probabilities should equal to 1 (i.e. 100%) if you have considered all possible combinations. (6 points)

Possible Outcome	Total Costs	Costs Paid by Each	Probability

2. Calculate the expected loss to each person before and after entering into a pooling arrangement. (4 points)
3. Calculate the standard deviation of the loss distribution to each person before and after entering into a pooling arrangement. What happens to the standard deviation after the pooling arrangement? (4 points)
4. What is the standard deviation if we increase the pool size to 100 million? (1 points)