Law of Large Numbers
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
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