Let X and Y be i.i.d. Unif(0, 1), and let W = X Y. (a) Find the mean and variance of W, without yet deriving the PDF. (b) Show that the distribution of W is symmetric about 0, without yet deriving the PDF. (c) Find the PDF of W. (d) Use the PDF of W to verify your results from (a) and (b). (e) How does the distribution of W relate to the distribution of X + Y , the Triangle distribution derived in Example? Give a precise description, e.g., using the concepts of location and scale.