In the transmission of digital information, the probability that a bit has high, moderate, or low distortion is 0.03, 0.05, and 0.92. 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 three transmitted, respectively. Determine the following (round all of your answers to 4 decimal places): (a) The probability that two bits have high distortion and one has moderate distortion. i (b) The probability that all three bits have low distortion. (c) The probability distribution, mean, and variance of X. Distribution: x fx(x) 1 2 i i 3 i 0 i Mean: E(X) = 1 (d) The conditional probability distribution, conditional mean, and conditional variance of X given that Y = 2. Distribution: X fx|Y=2(x) i i Variance: V(X) = Mean: E(X | Y = 2) = i Variance: V(X | Y = 2) = i
In the transmission of digital information, the probability that a bit has high, moderate, or low distortion is 0.03, 0.05, and 0.92. 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 three transmitted, respectively. Determine the following (round all of your answers to 4 decimal places): (a) The probability that two bits have high distortion and one has moderate distortion. i (b) The probability that all three bits have low distortion. (c) The probability distribution, mean, and variance of X. Distribution: x fx(x) 1 2 i i 3 i 0 i Mean: E(X) = 1 (d) The conditional probability distribution, conditional mean, and conditional variance of X given that Y = 2. Distribution: X fx|Y=2(x) i i Variance: V(X) = Mean: E(X | Y = 2) = i Variance: V(X | Y = 2) = i
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 7E
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Transcribed Image Text:In the transmission of digital information, the probability that a bit has high, moderate, or low distortion is 0.03, 0.05, and 0.92.
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 three transmitted, respectively. Determine the following (round
all of your answers to 4 decimal places):
(a) The probability that two bits have high distortion and one has moderate distortion. i
(b) The probability that all three bits have low distortion.
(c) The probability distribution, mean, and variance of X.
Distribution:
x fx(x)
1
2
i
i
3 i
0
i
Mean: E(X) =
1
(d) The conditional probability distribution, conditional mean, and conditional variance of X given that Y = 2.
Distribution:
X fx|Y=2(x)
i
i
Variance: V(X) =
Mean: E(X | Y = 2) = i
Variance: V(X | Y = 2) = i
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