From help-request at octave dot org Tue Sep 27 02:30:35 2005
Subject: Re: Determining if samples are normal
From: Michael Creel <michael dot creel at uab dot es>
To: "Robert A. Macy" <macy at california dot com>
Cc: Przemek Klosowski <przemek at jazz dot ncnr dot nist dot gov>, help@octave.org,         Quentin Spencer <qspencer@ieee.org>
Date: Tue, 27 Sep 2005 11:26:56 +0000

Robert A. Macy wrote:

>Right!  
>
>checked empirically using x=rand(1,1000) and hist(x) 
>it's there all right.  
>
>Didn't make sense at first then I remembered
>.5 + .5 done four different ways only reinforces the
>average, but...
>
>+0 +1
>+0 0
>1 0
>or,
>1 1
>
>rarely enhances the edges but definitely moves the
>weighting towards the average.  
>
>Learn something everyday.  
>
>
>So what is the PDF if the two are multiplied?
>
>              - Robert -
> 
>
>  
>
This is related to the central limit theorem. The average of the sum of 
n centered random variables, multiplied by the square root of n, 
converges in distribution to a normal random variable. There are a few 
technical conditions that need to be satisfied, but they hold for this 
example. There is no such general result for multiplication of random 
variables.



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