1. The problem statement, all variables and given/known data 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| ? 2. Relevant equations Nothing special. 3. 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!