Overview
The central limit describes the fact that a sum of a large number of i.i.d. random variables converges to a normal distribution.
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
This may take a moment - generating normals