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.

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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