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 "longterm average when sampling repeatedly".
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