Problem 5-K. Illustrating Distribution of a Linear Combination of Correlated Random Variables. A retailer purchases various products from a supplier, at costs represented by $ X, and sells them for :3 Y, thus making a prot :3 Z = Y X on each product. Based on the observations that (i) the purchase price of the product can only be positive (X 12 0); and (ii) the sale price of a product cannot be below the purchase price 01' 2 X); (iii) the number of sales fall exponentially as the selling price Y of a product increases, the retailer constructs a simple probability model for his business, based on the following joint probability density function for the purchase price X and sale price Y of a product: e'y for0