Hello,

I think I'm missing something silly here, but I'm stuck in a rut - a push would be appreciated.

I'm working with this distribution

I want to find the mean and variance. Often it's easy to convert

into something that looks like

where

is some pdf and therefore integrates to 1.

I didn't see a solution like this, so I went brute force and just tried to integrate it figuring it's probably not the most elegant way, but it should work.

using 'by parts':

I then try to do by parts again, but it's already clear that when I later go to evaluate the result between 0 and

the first x^3 term will blow up and there aren't any other convenient x^3 terms to cancel it out later.

Thanks!