Let $A$ and $B$ be identical, independent random variables with probability density functions (PDF) $f_A(a)$ and $f_B(b)$. Let $C = AB$. Why is the PDF of $C$ not $f_A(a)f_B(b)$?
Aren't $A$ and $B$ independent? Apparently, I'm supposed to not have the variables $a$ and $b$ in the PDF of $C$. Why is that? What is the right way to find the PDF of $C$?