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Article #211Re: SLLN and CLT for dble. index RV ?
From: USENET News System
Date: Wed, 15 Apr 1992 22:04
Date: Wed, 15 Apr 1992 22:04
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1435 bytes
In article <1992Apr15.053451.25886@newshost.anu.edu.au>, Andrew.Robinson@anu.edu.au writes:
>
> In article <1992Apr15.081401.1@cc.newcastle.edu.au> eemn@cc.newcastle.edu.au
> (Brett Ninness) writes:
> [...]
> >X_1,X_2,.........X_k
> >
> >are different to the variances of the X_j in
> >
> >X_1,X_2,.........X_k,X_{k+1}.
> >
> >To put it another way, the variance of a particular X_k depends on how
> >may terms I have in the sequence, hence the double indexing. All the terms
> >are zero mean and independent no matter how long the sequence.
> >
> I'm intrigued. How can you get a sequence of random variables whose values are
> independent, but whose variances depend on the number of values in the
> sequence?
>
Easily, if k is chosen first, and then the sequence is observed.
However, if you normalise the sequence, and let the normalised sequence be
Y_1, Y_2, ..., Y_k
can't you apply the CLT to the Y's?
Terry Moore, Massey University
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Path: arc1-ca.pugleaf.net!sparky!uunet!wupost!waikato.ac.nz!comp.vuw.ac.nz!cc-server4.massey.ac.nz!TMoore@massey.ac.nz Newsgroups: sci.math.stat Subject: Re: SLLN and CLT for dble. index RV ? Message-ID: <1992Apr15.220444.10907@massey.ac.nz> From: news@massey.ac.nz (USENET News System) Date: Wed, 15 Apr 92 22:04:44 GMT References: <1992Apr15.081401.1@cc.newcastle.edu.au> <1992Apr15.053451.25886@newshost.anu.edu.au> Organization: Massey University Lines: 28