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4. (15 points) A binary transmission system transmits a signal X. X has four possible values: 0, 1/3, 2/3, 1 with equal probability. The received

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4. (15 points) A binary transmission system transmits a signal X. X has four possible values: 0, 1/3, 2/3, 1 with equal probability. The received signal is Y=X+N, where N is the noise. (a) Assume the PDF of N is as follows f (n) = c 0.05 S n S 0.05 N 0 otherwise Find the value of c. (b) Suppose now N is a zero-mean Gaussian random variable with standard deviation o= 0.001. What is the probability that 1/3

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