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I'm studying statistics, and would like to better understand the Central Limit Theorem. The proof I found on Wikipedia requires some previous knowledge I do not currently possess.

Is there a quick intuitive explanation you can give as to why this theorem is correct?

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    Have you seen [this](http://stats.stackexchange.com/questions/3734) already?2010-12-04
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    @J. M., thanks for the link. Although, I didn't find a quick explanation that I understood, sadly. Specifically, I'm interested in why sampling any distribution (even a non-symmetric one) will lead to a normal, symmetric distribution, for large enough samples.2010-12-04
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    http://en.wikipedia.org/wiki/Illustration_of_the_central_limit_theorem might help provide a little intuition. Great question, by the way!2010-12-04
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    Not to confuse you, but the CLT only applies in the finite second moment case (finite variance). Levy-Stable distributions are also a convergent distribution of sums of random variables.2010-12-04

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