2. [Communication in Gaussian Noise] A wireless communication system consists of a transmitter and a receiver. The transmitter sends a signal x, and the receiver observes Y = x+Z, where Z is a noise term, modeled as a Gaussian random variable with mean z variance = 1. I = 0 and (a) Suppose the transmitted signal is x = 1. What is the pdf of the received signal Y? (b) Now suppose the transmitted signal can be either z = 1 or x = 1. The receiver uses the following decoding rule: if Y > 0, it declares that x = 1; if Y