= Law of large numbers
{title2=$\overline X_n\to\mathbb E X_1$}
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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 $\mathbb E|X_1|<\infty$, 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.
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