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Re: Expected value of the Geometric distribution

Started byDavid Skulsky <edskulsky@gmail.com>
First post2011-05-04 10:32 +0000
Last post2011-05-04 10:32 +0000
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  Re: Expected value of the Geometric distribution David Skulsky <edskulsky@gmail.com> - 2011-05-04 10:32 +0000

#2074 — Re: Expected value of the Geometric distribution

FromDavid Skulsky <edskulsky@gmail.com>
Date2011-05-04 10:32 +0000
SubjectRe: Expected value of the Geometric distribution
Message-ID<ipr9v7$q0$1@smc.vnet.net>
Mathematica has provided the simplest form of the result given what it knows about \Beta and \Mu.

If you provide it some additional information (via Assuming) and then Simplify, you will get what you expect:

int = Integrate[E^(-E^(-((x - \[Mu])/\[Beta])) - (x - \[Mu])/\[Beta])/\[Beta]* x, {x, -\[Infinity], \[Infinity]}]

Assuming[{Re[\[Beta]] > 0, \[Mu] > \[Beta]}, Simplify[int]]

EulerGamma \[Beta] + \[Mu]


David

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