Problem: Using the Neyman-Pearson Lemma, determine the most powerful test of size $ 5 \% $.
I know the Neyman-Pearson Lemma says that the test with the critical region $$ \left\{ x \in \{ 1,2,3,4 \} ~ \Bigg| ~ \frac{L(x \mid \theta = 0)}{L(x \mid \theta = 1)} \leq A \right\}, $$ where $ A $ satisfies $$ \mathbf{Pr} \left( \frac{L(X \mid \theta = 0)}{L(X \mid \theta = 1)} \leq A ~ \Bigg| ~ H_{0} \right) = 0.05, $$ is the most powerful test of size $ 5 \% $. However, I’m not sure what the likelihood functions are, as I’m more used to seeing them given by a formula.
Thanks.