This is the information I have, I want to test the hypotheses $H_0$ : λ = λ0 against the alternative hypotheses $H_0$ : λ = λ1, where λ1 > λ0.
I want to do this by using the Neyman–Pearson Lemma, and that rejecting $H_0$ if M < t is a most powerful test, where M =∑ $X_k$. ( if M < t we reject, not accept).
So far I've calculated the likelihood ratio as:
$\frac{\lambda_1}{\lambda_0}∑^n_{k=1}x^{n(d-1)}e^{-∑^n_{k=1}x(\lambda_1-\lambda_0)}$
How do I go from here with regards to the most powerful test?