### Detection and Estimation

Suppose you have a coin and you want to test two hypotheses: H0: the coin is fair (that is, you get a head with probability p = 0.5 and a tail with the same) and H1: the coin is unfair and has probability p > 05 for a head and (1-p) for a tail. Assume p is known. Explain in detail what the optimum Neyman = Pearson test is fo