2. Suppose we have a single observation from a $N\left(\theta, \theta^2 ight)$ distribution. (a) Derive the most powerful size $\alpha$ test for $$ H_0: \theta=1 $$ versus $$ H_1: \theta=\theta_1 $$ where $\theta_1$ is a fixed constant greater than 1. Derive the form of the test but you don't need to determine the exact threshold as a function of $\alpha$. (b) Determine whether the test you established above is uniformly most powerful level $\alpha$ for testing the hypotheses $$ H_0: \theta=1 $$ versus $$ H_1: \theta>1 $$