Law of large numbers


The law of large number is a law that states that the arithmetic mean of an iid random sample is guaranteed to converge to the expected value as the sample size becomes infinite.

More formally, the law actually has two statements: the strong law of large numbers and the weak law of large numbers.

> In other terms, given an arbitrarily small $\varepsilon$: > $$\lim_{ n \to \infty } P(\lvert \bar{X}_{n}-\mu \rvert \geq \varepsilon)=0

where PP is a measure of probability.

> In other terms, > $$P(\lim_{ n \to \infty } \bar{X}_{n}=\mu)=1

where PP is a measure of probability.