- 9 6. MAP and ML detection for scaling channel. If this problem, you will use the MAP and ML decision rules to design a signal detector. Alice sends X E {1,3} twice to Bob. Bob receives Yi ~ N(0,X) and Y2 ~ N(0, X2). In other words, Bob receives two Gaussian values, where the variance of the Gaussian values depend on the signal. Bob is given two samples (Y1, Y2) where both (Y1,Y2) are independently distributed according to N(0,1) if X = 1, or N(0,9) if X = 3. Let q denote the probability that X = 3, i.e., Px(3) q and Px(1) = 1-4, where 0