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Unformatted text preview: X and Y be given by f X,Y ( x,y ) = e-x y x < otherwise 1 Figure 1: Problem 6. Dene Z = X + Y , W = X-Y . Find the joint pdf of Z and W . Show that Z is not an exponential random variable. Problem 8. Let f X,Y ( x,y ) = 2 e-( x + y ) < x < y < otherwise Dene Z = X + Y , W = Y/X . Determine the joint pdf of Z and W . Problem 9. (a) Use the auxiliary variable method to nd the pdf of Z = X X + Y . (b) Find the pdf of Z if X and Y are independent exponential random variables with the same parameter . Problem 10. Suppose X and Y are zero-mean independent Gaussian random variables with common variance 2 . Dene R = X 2 + Y 2 and = tan-1 ( Y/X ), where | | < . Obtain their joint density function. 2...
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- Fall '08