I'm intrigued by the following idea but I don't know how to do it.
If I have a r.v. $x$ with given distribution $f_X(x)$ and I have a second variable $y=2x$. The goal is to find $f_Y(y)$.
I know the traditional solution, but, can I say that from $y=2x$, I can conclude that $f(y\mid x)=2x \cdot \delta(y-2x)$ ?? If that is correct, then I can form the joint $f(x,y)$ then I can marginalize out $x$ to reach my goal.
I'm trying to do it but I'm missing something.