In probability theory, the **weak law of large numbers** states that if *X*_{1}, *X*_{2}, *X*_{3}, ... is an infinite sequence of random variables, all of which have the same expected value μ and the same finite variance σ^{2}, and they are uncorrelated (i.e., the correlation between any two of them is zero), then the sample average

A consequence of the weak law of large numbers is the asymptotic equipartition property.

The **strong law of large numbers** states that if *X*_{1}, *X*_{2}, *X*_{3}, ... is an infinite sequence of random variables that are independent and identically distributed, and have a common expected value μ then

This law justifies the intuitive interpretation of the expected value of a random variable as the "long-term average when sampling repeatedly".