Suppose that we have that $Y=e^{aX}$ where $a$ is a positive scalar. We know that $Y$ follows a logNormal distribution with parameters $0$ and $2$. Then is there a way to derive the distribution of $X$??
From the definition, I think the $log(Y)=aX$ has to follow a normal distribution with mean $0$ and standard error $2$, but this distribution corresponds to $aX$. Thus, I would like to find a distribution of just $X$.
Something that came to my mind right now is that $aX$ (this kind of transformation) results to changes in the variance of the Normal distribution.