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Web crawlers need to estimate the frequency of changes to
Chapter 4, Problem 131E(choose chapter or problem)
Problem 131E
Web crawlers need to estimate the frequency of changes to Web sites to maintain a current index for Web searches. Assume that the changes to a Web site follow a Poisson process with a mean of 3.5 days.
(a) What is the probability that the next change occurs in less than 2.0 days?
(b) What is the probability that the time until the next change is greater 7.0 days?
(c) What is the time of the next change that is exceeded with probability 90%?
(d) What is the probability that the next change occurs in less than 10.0 days, given that it has not yet occurred after 3.0 days?
Questions & Answers
QUESTION:
Problem 131E
Web crawlers need to estimate the frequency of changes to Web sites to maintain a current index for Web searches. Assume that the changes to a Web site follow a Poisson process with a mean of 3.5 days.
(a) What is the probability that the next change occurs in less than 2.0 days?
(b) What is the probability that the time until the next change is greater 7.0 days?
(c) What is the time of the next change that is exceeded with probability 90%?
(d) What is the probability that the next change occurs in less than 10.0 days, given that it has not yet occurred after 3.0 days?
ANSWER:
Solution:
Step 1 of 5:
Let X follows a Poisson distribution with the density
P(X =x) =
Then, cdf is F(x) = 1 -
= 1 -
A web site follows a Poisson process with a mean of 3.5.