[[Convergence concepts in probability MOC]]
# Khinchin's law

Let $\overline{X}_{n}$ denote the [[𝜇-estimator|sample mean]] of a [[random sample]] of $n$ [[Independence of random variables|independent and identically distributed]] [[Real random variable|real random variables]] for each $n \in \mathbb{N}$.
Then $\overline{X}_{n}$ [[Convergence in probability|converges in probability]] to the true [[expectation]] $\mu$ as $n \to \infty$. #m/thm/prob 

> [!missing]- Proof
> #missing/proof

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