Consider a binary hypothesis-testing procedure where the two hypotheses H0 and H1 are described by different Poisson distributions, characterized by the parameters l0 and l1, respectively.
The observation is simply a number of events k, depending on whether H0 or H1 is true
where i = 0 for hypothesis H0 and i = 1 for hypothesis H1. Determine the log-likelihood ratio test for this problem.