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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

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

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.2: Probability
Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...
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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
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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