Problem 3 Consider the hypothesis pair Ho : Yk = Nk, k = 1, . ..,n versus H1 : Yk = Nk + OSk, k = 1, . ..,n where N ~ N(0, E), s is known, and O is a random variable indepen dent of N. (a) Find the a-level Neyman-Pearson detector and ROCs assuming that O is a discrete random variable taking the values +1 and -1 with equal probabilities (i.e., P(0 = +1) = P(0 = -1) = 1/2). (b) Suppose that O ~ N(0, ?). Assuming E = 21, show that the likelihood ratio is of the form L(y) = kiekalleyll2 where ki and k2 are positive constants. Find k2