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 two days?
(b) What is the probability that the next change occurs in greater than seven 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 days, given that it has not yet occurred after three days?
(a) The probability that the next change occurs in less than two days is 0.3085.
(b) The probability that the next change occurs in greater than seven days is 0.0067.
(c) The time of the next change that is exceeded with probability 90% is 6.02 days.
(d) The probability that the next change occurs in less than 10 days, given that it has not yet occurred after three days, is 0.9072.