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? (a) less than 20 days (b) more than 50 days (c) between 30 and 70 days
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? (a) less than 20 days (b) more than 50 days (c) between 30 and 70 days
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
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
(a) less than 20 days
(b) more than 50 days
(c) between 30 and 70 days
![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/B is a curve representing the exponential distribution. Areas under this curve give us exponential
probabilities.
y
a
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) = e¯a/ß - e-b/ß
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.
µ = B and o = ß
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 2 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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb11474ed-9b9e-4c4f-9aff-ec3ba6a44683%2Fee28bd75-f46c-470e-8f36-48275b244be6%2Fyh0v6hf_processed.png&w=3840&q=75)
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/B is a curve representing the exponential distribution. Areas under this curve give us exponential
probabilities.
y
a
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) = e¯a/ß - e-b/ß
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.
µ = B and o = ß
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 2 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:(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 < ∞) Hint: e = 0 (Round your answer to four decimal places.)
(c) between 30 and 70 days (Round your answer to four decimal places.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman