
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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![We wish to send a single 0 or 1 (perhaps, "no" or "yes" or "don't attack" or "attack"
or whatever) over what is called a noisy channel: a data transmission method in which
there is some probability p that any 0 will be changed to (that is, received as) a 1 and
the same probability that any 1 sent will be changed to a 0. A very primitive model
of what is called an "error correcting code" is the following: we will send same single
digit message n times, where n is odd, and "majority wins:" if more 0's are received
than l's, the message is viewed as having been a 0, and vice versa. Suppose p = .1 and
we take n = 7; let S be the random variable keeping track of whether the message was
in fact received correctly (that is, what is deduced at the receiving end is what was
actually sent). Find the probability mass function for S. Here is new work: first,
find E[S]. Second, find the expected value of the number of errors made.](https://content.bartleby.com/qna-images/question/da63cab4-88d3-4edb-a383-276dcabb839a/295015ad-dcee-4c19-a7cc-3acafcb61c0a/fy37a1_thumbnail.jpeg)
Transcribed Image Text:We wish to send a single 0 or 1 (perhaps, "no" or "yes" or "don't attack" or "attack"
or whatever) over what is called a noisy channel: a data transmission method in which
there is some probability p that any 0 will be changed to (that is, received as) a 1 and
the same probability that any 1 sent will be changed to a 0. A very primitive model
of what is called an "error correcting code" is the following: we will send same single
digit message n times, where n is odd, and "majority wins:" if more 0's are received
than l's, the message is viewed as having been a 0, and vice versa. Suppose p = .1 and
we take n = 7; let S be the random variable keeping track of whether the message was
in fact received correctly (that is, what is deduced at the receiving end is what was
actually sent). Find the probability mass function for S. Here is new work: first,
find E[S]. Second, find the expected value of the number of errors made.
Expert Solution

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Step 1
Given,
p=0.1
n=7
s is the random variable keeping track of message whether received correctly
We have to find the probability mass function for s.
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