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Is sum of two normally distributed variables normally distributed?
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Konrad Viltersten
science forum addict


Joined: 27 Jun 2005
Posts: 79

PostPosted: Mon Jul 10, 2006 5:17 am    Post subject: Is sum of two normally distributed variables normally distributed? Reply with quote

Is sum of two normally distributed variables normally
distributed? I'd say so. Any linear combination of such
variables is supposed to be normally distributed itself.

However, i have reasons to believe that it is not totally
true. Are there some special requirements needed to be
fulfilled? Is it possible at all to create
X ~ N(mu_X,sigma_X) and Y ~ N(mu_Y,sigma_Y)
so that
X+Y !~ N(mu,sigma),
where !~ denotes "not distributed as"?

--
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Konrad
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Sleep - thing used by ineffective people
as a substitute for coffee

Ambition - a poor excuse for not having
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Konrad Viltersten
science forum addict


Joined: 27 Jun 2005
Posts: 79

PostPosted: Mon Jul 10, 2006 7:46 am    Post subject: Re: Is sum of two normally distributed variables normally distributed? Reply with quote

Quote:
Is sum of two normally distributed variables normally
distributed? I'd say so. Any linear combination of such
variables is supposed to be normally distributed itself.

It's not true. For example, let X be a normal random variable, and let
Y=sX where s takes the values plus or minus one each with probability 1/2,
and s and X are independent.

I don't see it. I try to imagine what it would look like
but the PDF i get in my head is very normal. What do i
miss here? Might it be the fact that X and Y are not
so very independent?

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Konrad
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Sleep - thing used by ineffective people
as a substitute for coffee

Ambition - a poor excuse for not having
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Reef Fish
science forum Guru Wannabe


Joined: 28 Apr 2005
Posts: 200

PostPosted: Mon Jul 10, 2006 5:47 pm    Post subject: Re: Reef Fish; Was: Re: Is sum of two normally distributed variables normally distributed? Reply with quote

Stephen J. Herschkorn wrote:
Quote:
Reef Fish:

Failure to respond will be taken to be an admission of false claims.


Mr. Fish has amply demonstrated that he is, at best, a madman. I end my
discussion with him.

Is this what you call your discussion?

SJH> Again, Dr. Full Professor A**hole Reef Fish

Quote:
--
Stephen J. Herschkorn sjherschko@netscape.net

What happened to the TITLES and "Accomplished" description
in your sig?

So says

Quote:
Stephen J. Herschkorn sjhersc...@netscape.net
*Accomplished* Math Tutor on the Internet and in Central New Jersey and Mahnattan

upon being asked,

Quote:
RF> What have you 'Accomplished'? Is "Math Tutor on the Internet"
RF> a Title? I thought it was a FUNNY JOKE! Is that a Title you
RF> include in your resume? FOr such an acccomplished probabilist,
RF> why are you languishing as a 'Math Tutor on the Internet'?
RF
RF> Enquiring mind wants to know.

Those are the questions of a "madman"? In questioning the sig

Quote:
Stephen J. Herschkorn sjhersc...@netscape.net
*Accomplished* Math Tutor on the Internet and in Central New Jersey and Mahnattan

I think not. But your continued evasion to explain your own sig
doesn't
need a descriptive term for anyone to know that what I said is true:

Quote:
Failure to respond will be taken to be an admission of false claims.

-- Reef Fish Bob.
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