First let me apologise for my poor english, it's not my first language.

Here is the joint density function:

I'm trying to find and subsequenty .

I started by finding the marginal density functions:

and

Integration isn't really my strong suit, but I think I'm on the right path here. Next, finding and

This seems really counter-intuitive, but I'm not sure what I'm doing wrong (or right for that matter). I'd really appreciate any help. Thanks in advance.