Let us say that $X$ is a normal random variable, given that its expected value is $0$ and variance is $1$ . How do we compute the density function of $Y= e^ X$?
What I think: Since expected value is $0$ and variance is $1$, $X$ is a standard normal variable, whose pdf is given as: $\frac{1}{\sqrt{2\pi}}e^{-x^2 / 2}$.