# Thread: Transormation of Lognormal RV

1. ## Transormation of Lognormal RV

Hi, i've been stuck on this problem for a day now, and I'm finally giving up. I'm given a lognormal variable X(with mu, and sigma^2) and Assume a transformation of Y = aX^b. I need to find the distribtuion of Y and the expected value. Whenever i go for an attempt i end up getting to p(ln(x)< 1/b *ln(y/a) i start to try to integrate and I get lost. anyone willing to walk me through this? The algeba/calculus involved is horrid.

2. ## Re: Transormation of Lognormal RV

Hey glambeth.

What have you tried? Have you tried the transformation theorem? If not you should try this (the transformation theorem is used to get the PDF of a function of a random variable as long as the function is invertible across the domain of the of the original random variable).

In terms of the expected value you can calculate E[aX^b] using the log-normal PDF. You can also use your new PDF, but you don't need to for this part.

Are you aware of the transformation theorem?

3. ## Re: Transormation of Lognormal RV

I ended up getting it. I was making it much more complex then needed to be. Eventually even derived the MGF.