Question: 1. (*) A portfolio contains 16 independent risks, each with a gamma distribution with parameters a = 1and () = 250. Give an expression using the incomplete gamma function for the probability that the sum of the losses exceeds 6,000. Then approximate this probability using the central limit theorem.
2. (*) The severities of individual claims have the Pareto distribution with parameters a = 8/3 and () = 8,000. Use the central limit theorem to approximate the probability that the sum of I00 independent claims will exceed 600,000.