Law of Large Numbers

The law of large numbers states that as the number of trials in a probability experiment increases, the average of the results obtained will converge to the expected value: \[ \bar{X}_n \rightarrow \mu \text{ as } n \rightarrow \infty \] where \( \bar{X}_n \) is the sample mean of \( n \) independent and identically distributed random variables, and \( \mu \) is the expected value.