Consider a trinary communication channel [STAR 1979] whose channel diagram is shown in Figure 1.P.6. For i = 1,2, 3 let T; denote the event "digit i is trans- mitted" and let R, denote the event “digit i is received." Assume that a 3 is transmitted 3 times more frequently than a 1, and a 2 is sent twice as often as 1. If a 1 has been received, what is the expression for the probability that a1 was sent? Derive an expression for the probability of a transmission error. P(R1IT1) =1- T1 R1 a / 2 a / 2 B/2 1-B
Consider a trinary communication channel [STAR 1979] whose channel diagram is shown in Figure 1.P.6. For i = 1,2, 3 let T; denote the event "digit i is trans- mitted" and let R, denote the event “digit i is received." Assume that a 3 is transmitted 3 times more frequently than a 1, and a 2 is sent twice as often as 1. If a 1 has been received, what is the expression for the probability that a1 was sent? Derive an expression for the probability of a transmission error. P(R1IT1) =1- T1 R1 a / 2 a / 2 B/2 1-B
A First Course in Probability (10th Edition)
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![Consider a trinary communication channel [STAR 1979] whose channel diagram
is shown in Figure 1.P.6. For i = 1,2, 3 let T; denote the event "digit i is trans-
mitted" and let R, denote the event “digit i is received." Assume that a 3 is
transmitted 3 times more frequently than a 1, and a 2 is sent twice as often as 1.
If a 1 has been received, what is the expression for the probability that a1 was
sent? Derive an expression for the probability of a transmission error.
P(R1IT1) =1-
T1
R1
a / 2
a / 2
B/2
1-B
T2
R2
B/2
y/2
y/2
1-y
T3
R3
Figure 1.P.6. A trinary communication channel: channel diagram](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed4d3315-b207-47e5-8975-8bfcf768b34a%2F9494a740-ae42-4b2f-9396-817e3f9272ee%2Fp7hcios_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider a trinary communication channel [STAR 1979] whose channel diagram
is shown in Figure 1.P.6. For i = 1,2, 3 let T; denote the event "digit i is trans-
mitted" and let R, denote the event “digit i is received." Assume that a 3 is
transmitted 3 times more frequently than a 1, and a 2 is sent twice as often as 1.
If a 1 has been received, what is the expression for the probability that a1 was
sent? Derive an expression for the probability of a transmission error.
P(R1IT1) =1-
T1
R1
a / 2
a / 2
B/2
1-B
T2
R2
B/2
y/2
y/2
1-y
T3
R3
Figure 1.P.6. A trinary communication channel: channel diagram
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