Law of large numbers

SSU

If data are i.i.d(independent and identically distributed), then their average converges to the true mean.

Strong LoLN - Let there be an infinite sequence of i.i.d lebesque integrable random variables with equal means $E(X_1)=E(X_2)=\cdots =\mu$, than $\frac{1}{n}(X_1+X_2+\cdots +X_n)\to \mu ,$as $n\to \infty$.

We say that mean is an Unbiased etimator of expected value. Variance decays with $\frac{1}{n}$.

Weak LoLN - sample mean converges in probability to true mean.