2. (4 points) Loss severity (X) follows an inverse exponential distribution with parameter A. It is assumed that A follows an exponential distribution with mean 0. Show that the unconditional distribution of X is an inverse Pareto distri- bution with parameters 7 = 1 and 0. Do this by determining the probability density function (pdf) of X, appropriately using the above inverse exponen- tial and exponential distributions, and identifying the result as the inverse Pareto pdf. You may use the following result from calculus, where c is a positive con- stant: fed = 12. The pdf of an inverse exponential distribution, with x > 0 and 0 > 0, is: f(x) = = x-20-0/x The pdf of an inverse Pareto distribution, with x > 0, 7 > 0, and 0 > 0, is: f(x) = 70x-1 (x + 0)(T+1).