Suppose that Kate and Anne enter into a pooling arrangement. Assume that both women have the following loss-distributions and that losses are independent.
$50,000 with probability 0.005
$20,000 with probability 0.01
Loss = $10,000 with probability 0.02
$ 0 with probability 0.965
a. 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.
b. Calculate the expected loss to each person prior to and subsequent to entering into a pooling arrangement.
c. What happens to the standard deviation of the distribution of losses to each individual subsequent to the pooling arrangement?