5. 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 R₂ denote the event "digit i is received." Assume that a 3 i 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 a 1 wa sent? Derive an expression for the probability of a transmission error. P(R171) =1-α R1 T1% a/2 α/2 B/2 1-ẞ R2 T29 ẞ/2 Y/2 Y/2 T3 1-y R3 Figure 1.P.6. A trinary communication channel: channel diagram
5. 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 R₂ denote the event "digit i is received." Assume that a 3 i 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 a 1 wa sent? Derive an expression for the probability of a transmission error. P(R171) =1-α R1 T1% a/2 α/2 B/2 1-ẞ R2 T29 ẞ/2 Y/2 Y/2 T3 1-y R3 Figure 1.P.6. A trinary communication channel: channel diagram
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![5. 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 a 1 was
sent? Derive an expression for the probability of a transmission error.
P(R1IT1) =1-oa
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%2F653a6d11-6512-400f-875b-a9bd6bc11d13%2F40f7cf96-edae-4a16-8160-4c78ae5b2033%2Fjxtwmy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. 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 a 1 was
sent? Derive an expression for the probability of a transmission error.
P(R1IT1) =1-oa
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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