2. Let X and Y be two continuous random variables with joint pdf fxy(x,y). Let U = XY. Prove that fu, the pdf of the random variable U, is given by fv(u) = fxv (1, 0)| ² | dv. Hint: Use the transformation (x,y) → (u, v) defined as u = xy, v = y to find first the joint pdf fuv(u, v) of the random vector (U, V).

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2. Let X and Y be two continuous random variables with joint pdf fxy(x, y). Let
U = XY. Prove that fu, the pdf of the random variable U, is given by
fv(u) = £xx (, v)| ² | dv.
=[#
Hint: Use the transformation (x, y) → (u, v) defined as u = xy, v = y to find first the
joint pdf fuv(u, v) of the random vector (U, V).
Transcribed Image Text:2. Let X and Y be two continuous random variables with joint pdf fxy(x, y). Let U = XY. Prove that fu, the pdf of the random variable U, is given by fv(u) = £xx (, v)| ² | dv. =[# Hint: Use the transformation (x, y) → (u, v) defined as u = xy, v = y to find first the joint pdf fuv(u, v) of the random vector (U, V).
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