1. Suppose x, and x, are two independent random variables each with an exponential distribution; f (x,)=e ; x, 20 ; f (x,)=e ; x, 20. Let Y, X, +X, X, and Y; X, +X, A) Find the joint probability density function fy,y, (Y,,y,) and the two marginals fy, (y,), fy, (9;). B) Are Y, and Y, also independent, justify your answer. C) Find the mean value and the variance for both random variables Y, and Y,.

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