       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)
• 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).
>