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Problem 3 (4 marks) Consider two continuous random variables X and Y whose joint pdf is given by f ( x, y ) = y ofty , X > 0, y> 0. (a) Determine the covariance between X- 2Y and Y - X2 . (b) Find and sketch the pdf of U =2-Y2. (c) Find and sketch the pdf of V = X + Y. (d) Find and sketch the pdf of W = max(X, Y)