Let U be as defined in Eq. (9.6.3), and suppose that it is desired to test the

Question:

Let U be as defined in Eq. (9.6.3), and suppose that it is desired to test the hypotheses in Eq. (9.6.9). Prove that each likelihood ratio test has the following form: reject H0 if |U| ≥ c, where c is a constant. First prove that (x, y) = (1+ v2)−(m+n)/2, where v was defined in Eq. (9.6.12).