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A communications channel transmits the digits 0 and 1.
Chapter 4, Problem 43P(choose chapter or problem)
Problem 43P
A communications channel transmits the digits 0 and 1. However, due to static, the digit transmitted is incorrectly received with probability .2. Suppose that we want to transmit an important message consisting of one binary digit. To reduce the chance of error, we transmit 00000 instead of 0 and 11111 instead of 1. If the receiver of the message uses “majority” decoding, what is the probability that the message will be wrong when decoded? What independence assumptions are you making?
Questions & Answers
QUESTION:
Problem 43P
A communications channel transmits the digits 0 and 1. However, due to static, the digit transmitted is incorrectly received with probability .2. Suppose that we want to transmit an important message consisting of one binary digit. To reduce the chance of error, we transmit 00000 instead of 0 and 11111 instead of 1. If the receiver of the message uses “majority” decoding, what is the probability that the message will be wrong when decoded? What independence assumptions are you making?
ANSWER:
Solution :
Step 1 of 1:
Given a communications channel transmits the digits 0 and 1.
We assume that each digit is received incorrectly independently of other digits.
Let X denotes the number of digits incorrectly transmitted.
Let X follows a binomial distribution with the parameter n, p.
So XBin(5, 0.2).
Our goal is:
We need to find the probability that the message will be wrong when decoded.