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Suppose that the log-ons to a computer network follow a
Chapter 4, Problem 116E(choose chapter or problem)
Problem 116E
Suppose that the log-ons to a computer network follow a Poisson process with an average of three counts per minute.
(a) What is the mean time between counts?
(b) What is the standard deviation of the time between counts?
(c) Determine x such that the probability that at least one count occurs before time x minutes is 0.95.
Questions & Answers
QUESTION:
Problem 116E
Suppose that the log-ons to a computer network follow a Poisson process with an average of three counts per minute.
(a) What is the mean time between counts?
(b) What is the standard deviation of the time between counts?
(c) Determine x such that the probability that at least one count occurs before time x minutes is 0.95.
ANSWER:
Solution :
Step 1 of 3:
Given a Poisson process with an average of three counts per minute.
The formula for the Poisson distribution is
P(X=x) =
Where
Our goal is:
a). We need to find the mean time between counts.
b). We need to find the standard deviation of time between counts.
c). We need to determine the x value.
a). The mean time between counts for poisson process is
We know that .
0.33 min
Therefore, the mean time between counts is 0.33 min.