3. (4 points) Insurance is purchased on brand new medical equipment that will provide reimbursement if the equipment fails within the first five years. It is assumed that the time-until-failure of the medical equipment follows a two-parameter Pareto distribution with shape parameter equal to 3 and scale parameter 0. The two-parameter Pareto distribution has a variance of 27. The insurance pays a fixed (not random) amount of C at the moment of failure if the medical equipment fails during the first or second year, and pays , at the moment of failure if the medical equipment fails during the third, fourth, or fifth year. The insurance pays zero if the medical equipment fails after the fifth year. Calculate C such that the expected insurance payment is 2000. 4. (3 points) Let X1 and X2 be independent random variables: (i) X1 follows a gamma distribution with shape parameter equal to 5 and scale parameter equal to 1. (ii) X2 follows a gamma distribution with shape parameter equal to 2 and scale parameter equal to 1. 0.5 Define a new random variable: Y = 3 X 2 Calculate: E(Y)