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X=0 X=1 Po P₁ 90 Y=0 Y=1 Suppose that a single binary digit (0 or 1) is to be transmitted through a transmission channel. Because of the noise in the channel, the received binary digit can be in error. A schematic of a probabilistic model for this situation is shown in the figure below, for which P[X=0]=q, P[X=1] =p=1-q₂ and P[Y=0/X=0]=Po P[Y=1/X=0] =q=1 - Po P[ Y = 0/ X = 1 ] =q₁ = 1- P₁ P[Y=1/X=1] = P₁ where X is the transmitted digit and Y is the received digit. a) Determine the probability that the digit 1 is received. b) Determine the probability that an error occurs, given that the digit 1 was transmitted. c) Determine the unconditional probability of error.

X=0 X=1 Po P₁ 90 Y=0 Y=1 Suppose that a single binary digit (0 or 1) is to be transmitted through a transmission channel. Because of the noise in the channel, the received binary digit can be in error. A schematic of a probabilistic model for this situation is shown in the figure below, for which P[X=0]=q, P[X=1] =p=1-q₂ and P[Y=0/X=0]=Po P[Y=1/X=0] =q=1 - Po P[ Y = 0/ X = 1 ] =q₁ = 1- P₁ P[Y=1/X=1] = P₁ where X is the transmitted digit and Y is the received digit. a) Determine the probability that the digit 1 is received. b) Determine the probability that an error occurs, given that the digit 1 was transmitted. c) Determine the unconditional probability of error.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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X=0 X=1 Po P₁ 90 Y=0 Y=1
Transcribed Image Text:X=0 X=1 Po P₁ 90 Y=0 Y=1
Suppose that a single binary digit (0 or 1) is to be transmitted through a transmission channel. Because of the noise in the channel, the received binary digit can be in error. A schematic of a probabilistic model for this situation is shown in the figure below, for which P[X=0]=q, P[X=1] =p=1-q₂ and P[Y=0/X=0]=Po P[Y=1/X=0] =q=1 - Po P[ Y = 0/ X = 1 ] =q₁ = 1- P₁ P[Y=1/X=1] = P₁ where X is the transmitted digit and Y is the received digit. a) Determine the probability that the digit 1 is received. b) Determine the probability that an error occurs, given that the digit 1 was transmitted. c) Determine the unconditional probability of error.
Transcribed Image Text:Suppose that a single binary digit (0 or 1) is to be transmitted through a transmission channel. Because of the noise in the channel, the received binary digit can be in error. A schematic of a probabilistic model for this situation is shown in the figure below, for which P[X=0]=q, P[X=1] =p=1-q₂ and P[Y=0/X=0]=Po P[Y=1/X=0] =q=1 - Po P[ Y = 0/ X = 1 ] =q₁ = 1- P₁ P[Y=1/X=1] = P₁ where X is the transmitted digit and Y is the received digit. a) Determine the probability that the digit 1 is received. b) Determine the probability that an error occurs, given that the digit 1 was transmitted. c) Determine the unconditional probability of error.
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