- #1
tennesseewiz
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Homework Statement
A communications channel transmits the digits 0 and 1. However, due to static, the digit transmitted is incorrectly received with probability 0.2. 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?
Homework Equations
This problem is in the Random Variables chapter of our book, but I don't see how we should use a random variable here. Maybe let X={the number of incorrectly received digits in a string of five equal digits}?
The Attempt at a Solution
I've been told the solution is 0.942, but I have no idea why. When I looked at it, what I wanted to do was:
(0.2)^5
Obviously that's wrong.