# Re: Bivariate Integrations/Assumptions error

• To: mathgroup@smc.vnet.net
• Subject: [mg10704] Re: Bivariate Integrations/Assumptions error
• From: Paul Abbott <paul@physics.uwa.edu.au>
• Date: Fri, 30 Jan 1998 04:24:39 -0500
• Organization: University of Western Australia
• References: <6ahmj1\$pf3@smc.vnet.net>

```Mary Lesperance wrote:

> Mathematica has trouble with bivariate integrations.  I tried the
> following:  (The answer is 1 for any real Phi and Psi - this is just
> the product of 2 normal densities)
>
>    f[x_,y_,\[Phi]_,\[Psi]_,n_]:=.5*Exp[-.5*((x-\[Phi])^2 + (y-(\[Phi]^2
> +   \[Psi]))^2)]/Pi

Replacing the inexact 0.5 by the exact 1/2 works better:

In[1]:=SetOptions[Integrate, GenerateConditions -> False];

In[2]:= Integrate[Exp[-(1/2)*((x - \[Phi])^2 +
(y - (\[Phi]^2 + \[Psi]))^2)]/(2*Pi),
{x, -Infinity, Infinity}, {y, -Infinity, Infinity}]

Out[2]= 1

Cheers,
Paul

____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907
mailto:paul@physics.uwa.edu.au  AUSTRALIA
http://www.pd.uwa.edu.au/~paul

God IS a weakly left-handed dice player
____________________________________________________________________

```

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