Re: New user - Integration domain question

*To*: mathgroup at smc.vnet.net*Subject*: [mg52625] Re: [mg52566] New user - Integration domain question*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Sun, 5 Dec 2004 02:08:01 -0500 (EST)*Reply-to*: hanlonr at cox.net*Sender*: owner-wri-mathgroup at wolfram.com

Needs["Statistics`MultinormalDistribution`"]; dist=MultinormalDistribution[ {0,0}, {{1,0},{0,1}}]; PDF[dist,{x,y}] E^((1/2)*(-x^2 - y^2))/(2*Pi) % /. x^2->r^2-y^2 1/(E^(r^2/2)*(2*Pi)) Integrate[2*Pi*r*%,{r,0,r}] 1 - E^(-(r^2/2)) or just using the function RegionProbability RegionProbability[dist, Ellipsoid[{0,0}, {r,r}]] 1 - E^(-(r^2/2)) Bob Hanlon > > From: Bod <none at none.ch> To: mathgroup at smc.vnet.net > Date: 2004/12/02 Thu AM 02:21:21 EST > To: mathgroup at smc.vnet.net > Subject: [mg52625] [mg52566] New user - Integration domain question > > Hello, > > I'm trying to integrate a gaussian over a circle (radius r) domain > (in the x-y plane) by the way of a double integral : > > 'Integrate[f[x, y], {x, 0, r}, {y, -Sqrt[r - x^2], Sqrt[r - x^2]}]' > and > 'Integrate[f[x, y], {x, -r, 0}, {y, -Sqrt[r - x^2], Sqrt[r - x^2]}]' > > Unfortunately, Mathematica v.5 does not seem to respond correctly > and returns 'SeriesData::csa' errors. > > Is there a simple way to solve this problem ? I expect to get > the volume of the gaussian located over the circle. > I'll then add offsets to the center of the circle (x0,y0). > > Many thanks for your answers. > > With kindest regards, > B. Oliver > >