Weak Law of Large Numbers

Theorem

Let

• $\{X_n\}$ : Sequence of random samples, with
  • Common mean $\mu$
  • Common variance ${\sigma }^2<\infty$
• ${\bar{X}}_n=\frac{1}{n}{\sum }_{i=1}^n{X}_i$

Then

$${\bar{X}}_n\stackrel{P}{\to }\mu$$