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sanctifier

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## Homework Statement

If the probability density function(p.d.f.) of a random variable X is f(x) = 1/6 * e

^{-|x|/3}where x is lying in (-∞,∞) and |-x| = x if x≥0, then what is the p.d.f. of the random variable Z = XY = X*|X| where Y = |X| ?

## Homework Equations

Nothing special.

## The Attempt at a Solution

Answer: h(z) = f(x) * g(y) where g(y) = 2 * 1/6 * e

^{-y/3}= 1/3 * e

^{-y/3}

Comment: Because for y=|x|, its range shrinks to half of x, i.e., (0,∞) instead of the oringinal (-∞,∞), consequently, its p.d.f. should be 2*f(x). It seems like if h(z) = f(x) * g(y) then X and Y are independent? I think this answer is wrong, anyone can help?

Thank you in advance!

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