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...

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Extracted text: 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 fyy, (y,,y,) and the two marginals , (y,), , (.). 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,.