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)
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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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71f6a4b8-527f-4030-b85a-828002701c6f%2F62daa819-0c84-4a1c-b69f-bd9719afc6ce%2Ffjzis0o_processed.png&w=3840&q=75)
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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