Overview
The Law of Large Numbers states that the sum if i.i.d. random variables converges to the expected value of the distribution that generated the numbers.
Formal Definition
Let {% X_1,...,X_n %} be independent random variables with mean {% \mu %} and variance {% \sigma^2 %} Define
{% \hat{X} = \frac{1}{n} \sum_i X_i %}
then
{% P(|\hat{X} - \mu| > \epsilon) \rightarrow 0 %}
as {% n \rightarrow \infty %}
Demonstration
copy