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Let X1 and X2 denote two independent random variables each with the exponential distribution with θ...

Let X1 and X2 denote two independent random variables each with the exponential distribution with θ = 2. Find the joint p.d.f. of Y1 = X1 and Y2 = X1 + X2. What is the support of Y1 and Y2 (i.e., what is the domain of the joint p.d.f., where f(y1, y2) 6= 0)? Are Y1 and Y2 independent?

math   Statistics-And-Probability   
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