Re: [Phys-l] Basic statistics

[Jack Uretsky <jlu@hep.anl.gov>]

Single or multiple makes no difference.  His statement is still correct. 
I suggest you check a statistics text and review the proof.

I've just checked the Handbook, and it appears that Wipedia is correct. 
However it does not approach n(0,1), as other distributions do.

On Sat, 11 Nov 2006, Bernard Cleyet wrote:

> I think you two are "talking (writing) past each other".    One is a
> single distrib. tother several independent.  Furthermore, Wiki, claims
> that the Chi-square also does tend towards normalcy, but VERY slowly, as
> the # of DOF increases.
>
> http://en.wikipedia.org/wiki/Chi-square_distribution
>
>
> bc
>
>
>
>
>
> Jack Uretsky wrote:
>
> > As already pointed out, the central limit theorem does not apply to all
> > distributions.  You must state the theorem carefully.  In the case of the
> > chi-square distribution it is easy to demonstrate by example with MathCad
> > or a similar program that the large N limit is not Gaussian.
> > 					Regards,
> > 						Jack
> >
> > On Fri, 10 Nov 2006, Polvani, Donald G. wrote:
> >
> >
> >
> > > Jack Uretsky wrote:
> > >
> > >
> > >
> > > > This is a misconception. There are many distributions that become
> > > Gaussian in the large N limit, but not all.
> > >
> > >
> > > > The chi-squared distribution is an example of one that does not.
> > > However, for the SUM of independent, identically distributed random
> > > variables, each with mean mu and variance sigma^2, the central limit
> > > theorem tells us that the distribution (of the sum) tends to a Gaussian
> > > as N approaches infinity.
> > >
> > > Don Polvani
> > > Northrop Grumman Corp.
> > > Undersea Systems
> > > Annapolis, MD 21404
> > > _______________________________________________
> > > Forum for Physics Educators
> > > Phys-l@carnot.physics.buffalo.edu
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