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From: | Quentin Spencer |
Subject: | Re: Determining if samples are normal |
Date: | Mon, 26 Sep 2005 12:42:47 -0500 |
User-agent: | Mozilla Thunderbird 1.0.6-1.1.fc4 (X11/20050720) |
Robert A. Macy wrote:
Sorry, to jump in where I have very little knowledge and understanding, but doesn't the sum preserve the distribution? Seems counter intuitive to have the sum change the distribution if it's identical. Isn't it multiply that makes it triangular?
The PDF of a sum of two random variables is the convolution of their respective PDFs. It just happens that the convolution of a gaussian function with a gaussian function is a gaussian function (you could say that it is to convolution what the exponential function is to integration/differentiation), so the sum of two normals is also normal (but with a different variance), but the sum of any two other random variables is definitely not normal.
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