Question

Consider the random variables X and Y with the following joint probability density function: fX,Y (x,...

Consider the random variables X and Y with the following joint probability density function:
fX,Y (x, y) = xe-xe-y, x > 0, y > 0
(a) Suppose that U = X + Y and V = Y/X. Express X and Y in terms of U and V .
(b) Find the joint PDF of U and V .
(c) Find and identify the marginal PDF of U
(d) Find the marginal PDF of V
(e) Are U and V independent?

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