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kaushik.sinha...@gmail.com  
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 More options Jul 24, 5:38 am
Newsgroups: sci.math
From: kaushik.sinha...@gmail.com
Date: Wed, 23 Jul 2008 14:38:24 -0700 (PDT)
Local: Thurs, Jul 24 2008 5:38 am
Subject: simple probability question
I found this result in a research paper. not sure how to derive it.
any help??
suppose an n dimensional unit vector v=(v1,v2,...,vn) is chosen
uniformly at random from an n dimensional unit sphere. clearly
v1^2+v2^2+...+vn^2=1-----------------(1)
Then for any delta>0, with probability at least (1-delta) , we have
v1^2>=1/(n*log(1/delta))

This means that we have to show that the probability,  P[v1^2<1/
(n*log(1/delta))] is bounded by delta

I don't know how to show this but what I can see is that there exists
one i, such that vi^2>=1/n ...


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