The Pareto distribution has been used in economics as a model for a density function with a slowly decaying tail: ' "' f($) = Grass9'1, x 2 3:0 > 0, 9 > 0. Let X be a random variable having the Pareto distribution. 1. Find E(X) and E(X2). What constraints do you need to place on 6 for E(X) to exist? for E(X2) to exist? 2. Find the density of Y = lop;( X / :30). Can you identify the distribution of Y