申論題

1. If X is a random variable with Pareto distribution, then the probability that X is greater than some number x, ie. the complementary CDF, is given by

, where x_m is the (necessarily positive) minimum possible value of X, and a is a positive parameter.

(c) What is the moment generating function of X, , where t ≤ O? (10 points) Hint: Use incomplete gamma function: