4. (15 points) Consider the normal distribution N (0, ), where > 0 is the parameter. Sup- pose we have simple hypotheses H0 : = 0, H1 : = 1, where 1 > 0. Suppose we perform hypothesis testing based on n i.i.d. samples. Derive, for each confidence level (0, 1), the optimal critical region C given by the Neyman-Pearson lemma. Note: You also need to give an expression of any critical value involved.