On the wikipedia page for the product distribution, https://en.wikipedia.org/wiki/Product_distribution, it says that the pdf for $Z = XY$ is $f_{Z}(z)=\int _{{-\infty }}^{{\infty }}f_{X}\left(x\right)f_{Y}\left(z/x\right){\frac {1}{|x|}}\,dx.$ I'm curious about where the ${\frac {1}{|x|}}$ comes from because intuitively, for every Z, the probability Z = XY is equal to the probably X = x multiplied by the probability Y = z/x, implying that the pdf should just be $f_{Z}(z)= \int _{{-\infty }}^{{\infty }}f(x,z/x) = \int _{{-\infty }}^{{\infty }}f_{X}\left(x\right)f_{Y}\left(z/x\right)$
Thanks