I would use MGFs.
use and
Then
Plug in and by division you have the MGF of Y.
If X and Y are independent random variables, X having a chi-square distribution with 3 degrees of freedom, and X+Y having a chi-square dist with 7 degrees of freedom, prove that Y has chi-square dist with 4 degrees of freedom
Thank you for any help that can be provided
How do you know (aside from practice?) when to use mgf vs. anything else? We just looked at a getting the limiting distribution of
where
and the solution was best obtained using mgf. Thanks!
PS: I was able to do the problem, but had the hint do use mgf, so just trying to get a better sense of how to tackle these problems without hints.