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 signal are given by fx M=0(X) =. exp (- V2102 202 fx M=1(x) = exp - (x- 1)2 V2102 202 Suppose the received makes a 3-level decision as follows: Decide 0 was sent if Pr(M = 0|X = x) 2 0.9 Decide 1 was sent if Pr(M = 1|X = x) 2 0.9 Erase the symbol (decide IDK) if both Pr(M = 0|X = x) X1 , (c) the probabily that the received erases a symbol, (d) the probability that the receiver makes an error (i.e., decides a "0" was sent when a one was actually sent, or vice versa)