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MORE: Statistics`ContinousDistributions` (integrating over a UniformDistribution)
*To*: mathgroup at smc.vnet.net
*Subject*: [mg9252] MORE: Statistics`ContinousDistributions` (integrating over a UniformDistribution)
*From*: "decker, mark a" <ormad at orntsrv103.micro.lucent.com>
*Date*: Fri, 24 Oct 1997 01:01:06 -0400
*Sender*: owner-wri-mathgroup at wolfram.com
More on this....
I have just found out that putting the limits {x, 0, Pi} doesn't work
either!!!
When I try to calculate the MeanDist[] of the function Sin[x]
MeanDist[Sin[x]], I get a similar result whether or not I set the
limits to {x, 0, Pi}.
This puzzles me greatly since in the interval {0,Pi} the integrand
should merely be "Sin[x] (1/Pi)". Why can't Mathematica deal with it?
------------- for review -----------
><<Statistics`ContinuousDistributions`
>
>p[x_] := PDF[UniformDistribution[0,Pi],x]
>
>MeanDist[f_] := Integrate[ f p[x], {x, 0, Pi}]
MeanDist[ Sin[x] ] Doesn't give 2/Pi like I'd expect. (and I
don't even like forcing the limits to {0,Pi}... much better to have
{-infinity,infinity}
>===============================================================
>
><<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.
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