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 of $50,000 with probability 0.01
$1,000 with probability 0.03
$0 with probability 0.96

Required:
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 to 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? Support your answer. (HINT: You do not need to calculate standard deviations to answer this question.)