Probability | Part IA, 2004

The random variables X1X_{1} and X2X_{2} are independent, and each has an exponential distribution with parameter λ\lambda. Find the joint density function of

Y1=X1+X2,Y2=X1/X2Y_{1}=X_{1}+X_{2}, \quad Y_{2}=X_{1} / X_{2}

and show that Y1Y_{1} and Y2Y_{2} are independent. What is the density of Y2Y_{2} ?

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