Re: Problem to be solved (Product of Normal Distributions)

• To: mathgroup at smc.vnet.net
• Subject: [mg14166] Re: Problem to be solved (Product of Normal Distributions)
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Wed, 30 Sep 1998 02:04:15 -0400
• Sender: owner-wri-mathgroup at wolfram.com

>Imagine I have something like ax^2+bx+c. Now I want to know how to make
>Mathematica return me something in the form (x+d)^2, where d depends on
>a, b and c.
>
>This is the simple form. In reality I am trying to determine the sigma
>and mu of a product of the form
>
>        f_i=1/(sqrt(2 pi) sigma_i) Exp( -(x-mu_i)^2/(2 sigma_i^2)  )
>
>So I want to know what is the sigma and mu of f_1 times f_2.
>
>Now that you know it, I can also add that I tried Collect in every way,
>and some substituion rules.

Attached is one (semi-automatic) approach using pattern-matching and

Cheers,
Paul

"NormalDistribution.nb"

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Cell[TextData[{
"The product of ",
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Cell[BoxData[
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Note that, in general, the product is no longer correctly \ normalized.\
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