Suppose that the random variable X is transmitted over a communication channel Assume that the received signal is given by Y 2X W, where W N(0, 2 ) is independent of X Suppose that X 1 with probability p, and X 1 with probability 1 p The goal is to decide between X 1 and X 1 by observing the random variable Y Find the MAP test for this problem

Question: Suppose that the random variable X is transmitted over a communication channel. Assume that the received signal is given by Y = 2X +W, where

Suppose that the random variable X is transmitted over a communication channel. Assume that the received signal is given by Y = 2X +W, where W ∼ N(0,σ²) is independent of X. Suppose that X = 1 with probability p, and X = −1 with probability 1 −p. The goal is to decide between X = −1 and X = 1 by observing the random variable Y . Find the MAP test for this problem.

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