Let X1, ..., Xn be a random sample from a normal distribution, Xi ~ N(mu, 1).
a) Find a uniformly most powerful test of Ho: mu = mu(not) against Ha: mu < mu(not).
b) Find a uniformly most powerful test of Ho: mu = mu(not) against Ha: mu > mu(not).
c) Show that there is no uniformly most powerful test of Ho: mu = mu(not) against Ha: mu not = to mu(not).