The transformation theorem is based upon several assumptions (monotonicity, especially) that are valid for the pdf in exam.
Shortly and basically it says:
Hence:
where h(y) = log y, hence y>0.
Definition: a random variable Y is defined as Lognormal distributed if its logarithm is Normal distributed.
That means, given X=Log(Y) with
then
Well, I’m having very hard time to prove this. How can I go from the PDF of X to the pdf of Y?
In a previous post, Tukeywilliams says "use the transformation theorem to get the pdf of the lognormal". I tried unsuccesfully...
I would appreciate any help. Thanks!