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A digital communication system sends two messages M 0

A digital communication system sends two messages, M = 0 or M = 1, with equal probability. A receiver observes a voltage which can be modeled as a Gaussian random variable, X, whose PDFs conditioned on the transmitted message are given by

(a) Find and plot Pr (M = 0|X = x) as a function of for σ2 = 1. Repeat for σ2 =5.

(b) Repeat part (a) assuming that the a priori probabilities are Pr (M = 0) = 1/4 and Pr (M = 1) = 3/4.

(a) Find and plot Pr (M = 0|X = x) as a function of for σ2 = 1. Repeat for σ2 =5.

(b) Repeat part (a) assuming that the a priori probabilities are Pr (M = 0) = 1/4 and Pr (M = 1) = 3/4.

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