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