Please help with statistics question attached. In April 2011, an earthquake of magnitude 9+ struck Fukushima, Japan, causing catastrophic damage. Find a90% confidence interval for the expected time E until the next earthquake somewhere in the world that is assevere 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 behaveas a Poisson process, occurring at random times independent of each other, with a constant underlyingprobability of an event at any given moment. Take the units of time, conveniently, to be decades. Let X bethe number of such events in the past decade; by our assumption, X Poisson(2). Also, the times betweenthe events of a Poisson process are exponentially distributed with parameter 1 (that is, At) = te " for t> 0.)(a) Find P(X=0) (since there have been no earthquakes that severe in the past decade) in terms of a.

Name: Please help with statistics question attached. In April 2011, an earth
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Description: Please help with statistics question attached. In April 2011, an earthquake of magnitude 9+ struck Fukushima, Japan, causing catastrophic damage. Find a90% confidence interval for the expected time E until the next earthquake somewhere in the world t

Answered: (a) Find P(X=0) (since there have been…

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Please help with statistics question attached.

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 1 (that is, At) = te " for t> 0.)
(a) Find P(X=0) (since there have been no earthquakes that severe in the past decade) in terms of a.

Expert Solution

Step 1

E = expected time until next earthquake.

Times between the events of the process follow exponential distribution.

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