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Solved: Errors caused by contamination on optical disks
Chapter 4, Problem 143E(choose chapter or problem)
Problem 143E
Errors caused by contamination on optical disks occur at the rate of one error every 105 bits. Assume that the errors follow a Poisson distribution.
(a) What is the mean number of bits until five errors occur?
(b) What is the standard deviation of the number of bits until five errors occur?
(c) The error-correcting code might be ineffective if there are three or more errors within 105 bits. What is the probability of this event?
Questions & Answers
QUESTION:
Problem 143E
Errors caused by contamination on optical disks occur at the rate of one error every 105 bits. Assume that the errors follow a Poisson distribution.
(a) What is the mean number of bits until five errors occur?
(b) What is the standard deviation of the number of bits until five errors occur?
(c) The error-correcting code might be ineffective if there are three or more errors within 105 bits. What is the probability of this event?
ANSWER:
Solution :
Step 1 of 3:
Given the rate of one error every 105 bits.
We assume that the error follows a poisson distribution
Our goal is:
a). We need to find the mean number of bits until five errors occur.
b). We need to find the standard deviation of the number of bits until five errors occur.
c). We need to find the probability of events.
a). Let X denotes the number of bits until five errors.
We know that r=5 and error per bit.
The formula for the mean is
E(X) =
E(X) =
Therefore, the mean number of bits until five errors is .