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. Supposep = .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.
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. Supposep = .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.
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.
![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_processed.jpeg)
