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The Poisson distribution gives the probability for the number of occurrences for a "rare" event. - refer to screenshot (a) less than 20 days (i.e., x<=x<20) round to four decimal places. (b) more than 50 days

The Poisson distribution gives the probability for the number of occurrences for a "rare" event. - refer to screenshot (a) less than 20 days (i.e., x<=x<20) round to four decimal places. (b) more than 50 days

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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The Poisson distribution gives the probability for the number of occurrences for a "rare" event. - refer to screenshot

(a) less than 20 days (i.e., x<=x<20) round to four decimal places.

(b) more than 50 days

(a) less than 20 days (i.e., 0 < x < 20) (Round your answer to four decimal places.) (b) more than 50 days (i.e., 50 < x < 0) Hint: e = 0 (Round your answer to four decimal places.)
Transcribed Image Text:(a) less than 20 days (i.e., 0 < x < 20) (Round your answer to four decimal places.) (b) more than 50 days (i.e., 50 < x < 0) Hint: e = 0 (Round your answer to four decimal places.)
The Poisson distribution gives the probability for the number of occurrences for a "rare" event. Now, let x be a random variable that represents the waiting time between rare events. Using some mathematics, it can be shown that x has an exponential distribution. Let x > 0 be a random variable and let ß > 0 be a constant. Then y = =ex/ß is a curve representing the exponential distribution. Areas under this curve give us exponential probabilities. y If a and b are any numbers such that 0 < a < b, then using some extra mathematics, it can be shown that the area under the curve above the interval [a, b] is the following. P(a < x < b) = ea/ß - eb/B Notice that by definition, x cannot be negative, so, P(x < 0) = 0. The random variable x is called an exponential random variable. Using some more mathematics, it can be shown that the mean and standard deviation of x are the following. u = B and o = B Note: The number e = 2.71828. .. is used throughout probability, statistics, and mathematics. The key eš is conveniently located on most calculators. Comment: The Poisson and exponential distributions have a special relationship. Specifically, it can be shown that the waiting time between successive Poisson arrivals (i.e., successes or rare events) has an exponential distribution with B = 1/2, where 1 is the average number of Poisson successes (rare events) per unit of time. Fatal accidents on scheduled domestic passenger flights are rare events. In fact, airlines do all they possibly can to prevent such accidents. However, around the world such fatal accidents do occur. Let x be a random variable representing the waiting time between fatal airline accidents. Research has shown that x has an exponential distribution with a mean of approximately 44 days.t We take the point of view that x (measured in days as units) is a continuous random variable. Suppose a fatal airline accident has just been reported on the news. What is the probability that the waiting time to the next reported fatal airline accident is the following?
Transcribed Image Text:The Poisson distribution gives the probability for the number of occurrences for a "rare" event. Now, let x be a random variable that represents the waiting time between rare events. Using some mathematics, it can be shown that x has an exponential distribution. Let x > 0 be a random variable and let ß > 0 be a constant. Then y = =ex/ß is a curve representing the exponential distribution. Areas under this curve give us exponential probabilities. y If a and b are any numbers such that 0 < a < b, then using some extra mathematics, it can be shown that the area under the curve above the interval [a, b] is the following. P(a < x < b) = ea/ß - eb/B Notice that by definition, x cannot be negative, so, P(x < 0) = 0. The random variable x is called an exponential random variable. Using some more mathematics, it can be shown that the mean and standard deviation of x are the following. u = B and o = B Note: The number e = 2.71828. .. is used throughout probability, statistics, and mathematics. The key eš is conveniently located on most calculators. Comment: The Poisson and exponential distributions have a special relationship. Specifically, it can be shown that the waiting time between successive Poisson arrivals (i.e., successes or rare events) has an exponential distribution with B = 1/2, where 1 is the average number of Poisson successes (rare events) per unit of time. Fatal accidents on scheduled domestic passenger flights are rare events. In fact, airlines do all they possibly can to prevent such accidents. However, around the world such fatal accidents do occur. Let x be a random variable representing the waiting time between fatal airline accidents. Research has shown that x has an exponential distribution with a mean of approximately 44 days.t We take the point of view that x (measured in days as units) is a continuous random variable. Suppose a fatal airline accident has just been reported on the news. What is the probability that the waiting time to the next reported fatal airline accident is the following?
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