The Law of Large Numbers is a fundamental theorem in probability and statistics that describes the result of performing the same experiment a large number of times. It states that as the number of trials of a random experiment increases, the sample mean (or average) of the results will tend to converge to the expected value (the theoretical mean) of the underlying probability distribution.
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Laws of large numbers give conditions under which sample means approach a deterministic expected value. For independent and identically distributed random variables with , the strong law of large numbers gives almost sure convergence, while the weak law of large numbers gives convergence in probability. These conclusions specify different modes of convergence of random variables, rather than a universal numerical accuracy guarantee. The central limit theorem is a separate result about the remaining fluctuations after rescaling.