Answer: In the transmission of digital information, the

Chapter 5, Problem 5-12

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In the transmission of digital information, the probability that a bit has high, moderate, or low distortion is 0.01, 0.04, and 0.95, respectively. Suppose that three bits are transmitted and that the amount of distortion of each bit is assumed to be independent. Let X and Y denote the number of bits with high and moderate distortion out of the three transmitted, respectively. Determine the following: (a) The probability that two bits have high distortion and one has moderate distortion (b) The probability that all three bits have low distortion (c) The probability distribution, mean, and variance of X (d) The conditional probability distribution, conditional mean, and conditional variance of X given that Y 2