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Statistics`ContinousDistributions` (integrating over a UniformDistribution)
*To*: mathgroup at smc.vnet.net
*Subject*: [mg9250] Statistics`ContinousDistributions` (integrating over a UniformDistribution)
*From*: "decker, mark a" <ormad at orntsrv103.micro.lucent.com>
*Date*: Fri, 24 Oct 1997 01:01:03 -0400
*Sender*: owner-wri-mathgroup at wolfram.com
Hello helpful Mathematica people.
For fun (and to help introduce me to new features in Mathematica) I've
decided to work all the problems in a Q.M. text using only Mathematica
3.0.1. (I say this so you will understand I am not seeking the result,
but the *most elegant/general* method.
===============================================================
<<Statistics`ContinuousDistributions`
p[x_] := PDF[UniformDistribution[0,Pi],x]
MeanDist[f_] := Integrate[ f p[x], {x, -Infinity, Infinity}]
(* which gives *)
Integrate::idiv: Integral of (x(Sign[x] - Sign[-Pi+x]))/(2 Pi) does not
converge on {-Infinity, Infinity}.
Integrate::idiv: Integral of x (Sign[x] - Sign[-Pi+x]) does not converge
on {-Infinity, Infinity}.
Integrate[ x (Sign[x] - Sign[-Pi + x])/(2 Pi), {x, -Infinity,
Infinity}]
===============================================================
** again I'm not looking for the answer, I realize for this problem I
could just put in the limits {x, 0, Pi} and everything is fine.... but
would like to keep the function MeanDist[] general.
I know that the UniformDistribution is not a well behaved function (it's
derivative has infinities), but I'm hoping that I can have mathematica
solve this symbolically without requiring me to put in the limits {x,
0, Pi}.
Any help would be great.
Mark A. Decker
ormad at micro.lucent.com
D-Lab (AFM)
Lucent Technologies
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