Question 1 A simple binary communication channel carries messages by using two signals 0 and 1.It was assumed that for a given binary channel, 40% of the time a lis transmitted; the probability that a transmitted 0 is correctly received is 0.90; the probability that 1 is correctly received 0.95. This information is illustrated in Figure 1 where A= event that 1 is transmitted. A = event that 0 is transmitted. B= event that 1 is received. B = event that 0 is received.

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter20: Queuing Theory
Section20.6: The M/m/s/gd/∞/∞ Queuing System
Problem 14P
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A
Figure 1: A single- stage binary communication channel
Determine
P(B)and P(B)
b. P(A|B)
c. The stochastic matrix of the communication channel.
d. If P(B/A) - Р(C/В) and P(B/A) - Р(С)В), find
а.
P(C/B)
P(C/B)
i.
ii.
e. Figure 2 below illustrate information on a two- stage binary communication channel.
Copy and complete the channel with the necessary probabilities.
0.95
0.4
0.05
0.1
Figure 2
Use the information on Q1(d) to determine
f. Р(АВС)
8. Р(С)
h. Р(С)
i. Illustrate the two- stage binary communication channel on a tree diagram with their respective
probability.
Transcribed Image Text:A Figure 1: A single- stage binary communication channel Determine P(B)and P(B) b. P(A|B) c. The stochastic matrix of the communication channel. d. If P(B/A) - Р(C/В) and P(B/A) - Р(С)В), find а. P(C/B) P(C/B) i. ii. e. Figure 2 below illustrate information on a two- stage binary communication channel. Copy and complete the channel with the necessary probabilities. 0.95 0.4 0.05 0.1 Figure 2 Use the information on Q1(d) to determine f. Р(АВС) 8. Р(С) h. Р(С) i. Illustrate the two- stage binary communication channel on a tree diagram with their respective probability.
Question 1
A simple binary communication channel carries messages by using two signals 0 and 1.It was assumed that for
a given binary channel, 40% of the time a lis transmitted; the probability that a transmitted 0 is correctly
received is 0.90; the probability that 1lis correctly received 0.95. This information is illustrated in Figure 1
where
A= event that 1 is transmitted.
A = event that 0 is transmitted.
B= event that 1 is received.
B = event that 0 is received.
Transcribed Image Text:Question 1 A simple binary communication channel carries messages by using two signals 0 and 1.It was assumed that for a given binary channel, 40% of the time a lis transmitted; the probability that a transmitted 0 is correctly received is 0.90; the probability that 1lis correctly received 0.95. This information is illustrated in Figure 1 where A= event that 1 is transmitted. A = event that 0 is transmitted. B= event that 1 is received. B = event that 0 is received.
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