What is the probability that the next change occurs in less than 5.5 days? b. What is the probability that the time until the next change is greater 10.5 days? c. What is the time of the next change that is exceeded with probability 85%?
What is the probability that the next change occurs in less than 5.5 days? b. What is the probability that the time until the next change is greater 10.5 days? c. What is the time of the next change that is exceeded with probability 85%?
What is the probability that the next change occurs in less than 5.5 days? b. What is the probability that the time until the next change is greater 10.5 days? c. What is the time of the next change that is exceeded with probability 85%?
6. 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 7 days. Let a random variable X denote the time (in days) until the next change. a. What is the probability that the next change occurs in less than 5.5 days? b. What is the probability that the time until the next change is greater 10.5 days? c. What is the time of the next change that is exceeded with probability 85%? d. What is the probability that the next change occurs in less than 13 days, given that it has not yet occurred after 3.0 days?
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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