Poisson Generalised Likelihood Ratio Test

I am attempting Q19H from this document: https://www.maths.cam.ac.uk/sites/www.maths.cam.ac.uk/files/pre2014/undergrad/pastpapers/2014/ib/PaperIB_1.pdf I am alright with the first part, however, it asks me to derive a generalised likelihood ratio test for a pair of simple hypotheses - I thought that generalised likelihood ratio tests were only for composite hypotheses? Or am I to assume that the lambdas are unknown, and hence I need to calculate the maximum likelihood estimators of them under the null?

For the last part, I conclude to reject H0 since we have 2 degrees of freedom and 15.67 is much larger than the expected value of a chi squared distribution of 2. Is this correct?

• anyone can help me out? – MathematicianP May 12 at 13:12