Consider a binary hypothesis-testing procedure where the

Question

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.