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MathGroup Archive 1998

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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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