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 time between changes of 8 days. Let a random variable X denote the time (in days) until the next change. Round your answers to three decimal places (e.g. 98.765). a) What is the probability that the next change occurs in less than 6.5 days? P(X < 6.5) = i b) What is the probability that the time until the next change is greater 11.5 days? P(X > 11.5) = i c) What is the time of the next change that is exceeded with probability 90%? X = i day(s) d) What is the probability that the next change occurs in less than 14.5 days, given that it has not yet occurred after 3.0 days? P(X < 14.5|X > 3.0) = i

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