Question 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.  

P2SFWR The Asker · Probability and Statistics
 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.     
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