Central Limit Theorem
Overview
Formal Definition
Let {% X_1,..., X_n %} be a sequence of independent random variables drawn from a common distribution F with mean 0 and variance {% \sigma^2 %},
also with a moment generating function defined near zero.
{% S_n = \sum X_i %}
then
{% \lim_{n \rightarrow \infty} P(\frac{S_n}{\sigma \sqrt{n}} \leq x) = \mathbb{N}(x) %}
Demonstration
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