A binary communication channel transmits a sequence of “bits” (0s and 1s). Supposethat for any particular bit transmitted, there is a 10% chance of a transmission error (a0 becoming a 1 or a 1 becoming a 0). Assume that bit errors occur independently ofone another.a. Consider transmitting 1000 bits. What is the approximate probability that atmost 125 transmission errors occur?b. Suppose the same 1000-bit message is sent two different times independentlyof one another. What is the approximate probability that the number of errors inthe first transmission is within 50 of the number of errors in the second?

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 6E: Suppose the probability of erroneously transmitting a single digit is P=0.03. Compute the...
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A binary communication channel transmits a sequence of “bits” (0s and 1s). Suppose
that for any particular bit transmitted, there is a 10% chance of a transmission error (a
0 becoming a 1 or a 1 becoming a 0). Assume that bit errors occur independently of
one another.
a. Consider transmitting 1000 bits. What is the approximate probability that at
most 125 transmission errors occur?
b. Suppose the same 1000-bit message is sent two different times independently
of one another. What is the approximate probability that the number of errors in
the first transmission is within 50 of the number of errors in the second?

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