Consider a random sample X1,...Xn from a population X with support

on non-negative integers. A simple null hypothesis H0 assumes

that X has a Poisson distribution with mean 1. A simple alternative

hypothesis H1 assumes that X has a geometric distribution with mean

2.

a. Find a best critical region for testing H0 against H1.

b. Let n = 1 and the best critical region C = {0,3,4.....}. Compute the

level of significance and power.

Note: Please specify how Neyman Pearson Lemma can be correctly used to solve this question, considering the likelihood function in two hypotheses is different.