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Konrad Viltersten
science forum addict
Joined: 27 Jun 2005
Posts: 79
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 Posted: Mon Jul 10, 2006 5:17 am Post subject:
Is sum of two normally distributed variables normally distributed?
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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"?
--
Vänligen
Konrad
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Sleep - thing used by ineffective people
as a substitute for coffee
Ambition - a poor excuse for not having
enough sence to be lazy
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Konrad Viltersten
science forum addict
Joined: 27 Jun 2005
Posts: 79
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| Posted: Mon Jul 10, 2006 7:46 am Post subject:
Re: Is sum of two normally distributed variables normally distributed?
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| 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.
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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?
--
Vänligen
Konrad
---------------------------------------------------
Sleep - thing used by ineffective people
as a substitute for coffee
Ambition - a poor excuse for not having
enough sence to be lazy
--------------------------------------------------- |
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Reef Fish
science forum Guru Wannabe
Joined: 28 Apr 2005
Posts: 200
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| Posted: Mon Jul 10, 2006 5:47 pm Post subject:
Re: Reef Fish; Was: Re: Is sum of two normally distributed variables normally distributed?
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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.
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Is this what you call your discussion?
SJH> Again, Dr. Full Professor A**hole Reef Fish
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
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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.
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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
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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.
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-- Reef Fish Bob. |
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