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.