Show me a proof Proof of how the normal distribution arises as the limit of the binomial---where — where do $\pi$ and $e$ come from?

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occurred Apr 26, 2012 at 11:11

fixed your mathjax

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edited Apr 26, 2012 at 2:42

gung - Reinstate Monica

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Show me a proof of how the normal distribution arises as the limit of the binomial---where do pi$\pi$ and e$e$ come from?

I've always thought the emergence of the normal distribution was kind of magic, specifically that pi$\pi$ and e$e$ both emerge in the distribution, even though they don't exist in the binomial.

I've googled heavily, but haven't found a very good guide showing how these constants arise, but would like to see it.

I'm horrible at proofs, so can someone walk me through taking binomial to the limit to arrive at the normal? Wolfram says de Moivre developed this before 1783. Also, if possible, please don't use the CLT for the proof. Perhaps I'm wrong, but my understanding is that the CLT wasn't proven until the 19th century.

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edited Apr 26, 2012 at 2:03

Mittenchops

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Show me a proof of how the normal distribution arises as the limit of the binomial? Where---where do pi and e come from?

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asked Apr 26, 2012 at 1:58

Mittenchops

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Show me a proof Proof of how the normal distribution arises as the limit of the binomial---where — where do $\pi$ and $e$ come from?

Show me a proof of how the normal distribution arises as the limit of the binomial---where do pi$\pi$ and e$e$ come from?

Show me a proof of how the normal distribution arises as the limit of the binomial---where do pi and e come from?

Show me a proof of how the normal distribution arises as the limit of the binomial---where do $\pi$ and $e$ come from?

Show me a proof of how the normal distribution arises as the limit of the binomial? Where---where do pi and e come from?