Hi. I really don't find my lecture notes useful, and I can find precisely zero good guides online for how to deal with this.

The question is:

Given X1,...,Xn are Exp(a) and Y1,...,Yn are Exp(b) random variables, find the likelihood ratio test of size alpha of Ho: a=b against H1: a=/=b, expressing it in the form of the statistic:

T=(Sum Xi)/(SumXi+SumYi)

and the quantiles of a standard distribution.

My thoughts so far: Absolutely nothing. I have no idea whatsoever how to go about solving this question. And this is only Q2...

Thanks for any help.