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)

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...

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