times in succession. During each transmission, the probability is 0.995 that the digit entered will be transmit accurately. In other words, the probability is 0.005 that the digit being transmitted will be recorded with the opposite value at the end of the transmission. For each transmission after the first one, the digit entered for transmission is the one that was recorded at the end of the preceding transmission. If Xo denotes the binary digit entering the system, X₁ the binary digit recorded after the first transmission, X₂ the binary digit record after the second transmission, ..., then {X₂} is a Markov chain. (a) Construct the (one-step) transition matrix. (b) Find the 10-step transition matrix P(10). Use this result to identify the probability that a digit entering th network will be recorded accurately after the last transmission
times in succession. During each transmission, the probability is 0.995 that the digit entered will be transmit accurately. In other words, the probability is 0.005 that the digit being transmitted will be recorded with the opposite value at the end of the transmission. For each transmission after the first one, the digit entered for transmission is the one that was recorded at the end of the preceding transmission. If Xo denotes the binary digit entering the system, X₁ the binary digit recorded after the first transmission, X₂ the binary digit record after the second transmission, ..., then {X₂} is a Markov chain. (a) Construct the (one-step) transition matrix. (b) Find the 10-step transition matrix P(10). Use this result to identify the probability that a digit entering th network will be recorded accurately after the last transmission
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:7. Suppose that a communications network transmits binary digits, 0 or 1, where each digit is transmitted 10
times in succession. During each transmission, the probability is 0.995 that the digit entered will be transmitted
accurately. In other words, the probability is 0.005 that the digit being transmitted will be recorded with the
opposite value at the end of the transmission. For each transmission after the first one, the digit entered for
transmission is the one that was recorded at the end of the preceding transmission. If X₁ denotes the binary
digit entering the system, X₁ the binary digit recorded after the first transmission, X₂ the binary digit recorded
after the second transmission, then {X₂} is a Markov chain.
(a) Construct the (one-step) transition matrix.
(b) Find the 10-step transition matrix P(10). Use this result to identify the probability that a digit entering the
network will be recorded accurately after the last transmission.
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