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The joint p.d.f. of two random variables X 1 and X 2 is f ( x 1 , x 2 ) = { 2 e

The joint p.d.f. of two random variables X1 and X2 is

f(x1,x2)={2ex1ex2,for0<x1<x2<+}0, elsewhere

Consider the transformationY1=2X2,Y2=X1X2

a) Find the joint probability density function of Y1 and Y2

b) Find the marginal probability density functions of Y1 and Y2

c) Show and explain whether or not Y1 and Y2 are independent from each other

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