Question: In composite-hypothesis testing, we can obtain an upper bound on the test performance by assuming that the receiver first measures the unknown parameters perfectly and then design the optimum likelihood ratio test. Such a bound is called a perfect measurement bound. The ROC of any test will be bounded by the ROC of this fictitious perfect measurement test. Given that under H0 the observation Z is N(O, σ02) and under H1, Z is N(0, σi2) with σ1 > σ0, find the upper bound on the ROC for a PF of 10-1 and determine if a UMP test exists.