Homework Help is Here – Start Your Trial Now!
Math
Probability
In April 2011, an earthquake of magnitude 9+ struck Fukushima, Japan, causing catastrophic damage. Find a 90% confidence interval for the expected time E until the next earthquake somewhere in the world that is as severe as that one, using only the fact that there have been no such events in the past ten years. To do this, once again we need to make an assumption. The most neutral approach is to presume that such events behave as a Poisson process, occurring at random times independent of each other, with a constant underlying probability of an event at any given moment. Take the units of time, conveniently, to be decades. Let X be the number of such events in the past decade; by our assumption, X~ Poisson(2). Also, the times between the events of a Poisson process are exponentially distributed with parameter 2 (that is, f1) = de¯ª for t> 0.) (a) Find P(X=0) (since there have been no earthquakes that severe in the past decade) in terms of å. (b) Using your answer to (a) in the manner of a pivotal quantity, solve .05 < P(X=0)<.95 to obtain a 90% confidence interval for 2.

In April 2011, an earthquake of magnitude 9+ struck Fukushima, Japan, causing catastrophic damage. Find a 90% confidence interval for the expected time E until the next earthquake somewhere in the world that is as severe as that one, using only the fact that there have been no such events in the past ten years. To do this, once again we need to make an assumption. The most neutral approach is to presume that such events behave as a Poisson process, occurring at random times independent of each other, with a constant underlying probability of an event at any given moment. Take the units of time, conveniently, to be decades. Let X be the number of such events in the past decade; by our assumption, X~ Poisson(2). Also, the times between the events of a Poisson process are exponentially distributed with parameter 2 (that is, f1) = de¯ª for t> 0.) (a) Find P(X=0) (since there have been no earthquakes that severe in the past decade) in terms of å. (b) Using your answer to (a) in the manner of a pivotal quantity, solve .05 < P(X=0)<.95 to obtain a 90% confidence interval for 2.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
See similar textbooks
icon
Related questions
Question
100%

Can you please help with part (b) of statistics question attached

Please do not reject question if it is too complex for you and you do not know how to solve this problem.
Allow another expert a chance to answer this question.

In April 2011, an earthquake of magnitude 9+ struck Fukushima, Japan, causing catastrophic damage. Find a 90% confidence interval for the expected time E until the next earthquake somewhere in the world that is as severe as that one, using only the fact that there have been no such events in the past ten years. To do this, once again we need to make an assumption. The most neutral approach is to presume that such events behave as a Poisson process, occurring at random times independent of each other, with a constant underlying probability of an event at any given moment. Take the units of time, conveniently, to be decades. Let X be the number of such events in the past decade; by our assumption, X~ Poisson(2). Also, the times between the events of a Poisson process are exponentially distributed with parameter å (that is, ft) = de for t> 0.) (a) Find P(X=0) (since there have been no earthquakes that severe in the past decade) in terms of 2. (b) Using your answer to (a) in the manner of a pivotal quantity, solve .05 < P(X=0) <.95 to obtain a 90% confidence interval for å.
Transcribed Image Text:In April 2011, an earthquake of magnitude 9+ struck Fukushima, Japan, causing catastrophic damage. Find a 90% confidence interval for the expected time E until the next earthquake somewhere in the world that is as severe as that one, using only the fact that there have been no such events in the past ten years. To do this, once again we need to make an assumption. The most neutral approach is to presume that such events behave as a Poisson process, occurring at random times independent of each other, with a constant underlying probability of an event at any given moment. Take the units of time, conveniently, to be decades. Let X be the number of such events in the past decade; by our assumption, X~ Poisson(2). Also, the times between the events of a Poisson process are exponentially distributed with parameter å (that is, ft) = de for t> 0.) (a) Find P(X=0) (since there have been no earthquakes that severe in the past decade) in terms of 2. (b) Using your answer to (a) in the manner of a pivotal quantity, solve .05 < P(X=0) <.95 to obtain a 90% confidence interval for å.
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Basics of Inferential Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON
SEE MORE TEXTBOOKS