Question: Consider an additive noise channel Y = X + W. The signal (+1, with probability X = 3 -1, with probability 4 and the

Consider an additive noise channel Y = X + W. The signal (+1, with probability X = 3 -1, with probability 4

Consider an additive noise channel Y = X + W. The signal (+1, with probability X = 3 -1, with probability 4 and the noise W is a Gaussian with mean 0 and variance 4. The observation Y, the signal X and the noise W are independent. a. Write the MAP detection rule for X. b. Find an optimum threshold for a simpler detection rule. c. Find the probability of error in terms of Q functions.

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