In probability theory, the law of large numbers is a mathematical law stating that the average of the results obtained from a large number of independent, identically distributed random samples converges to the true expected value as the number of samples grows, provided that expected value exists. The result exists in two standard forms, the weak law and the strong law, which differ in the type of convergence they guarantee; this entity covers the general law encompassing both, which is why sample averages are treated as reliable estimates of a population mean.
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StatementThe law of large numbers is a mathematical law stating that the average of the results obtained from a large number of independent, identically distributed random samples converges to the true expected value as the number of samples grows, provided that expected value exists. 1 Classification
Statement FormCharacterization Theorem 1 Connections
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Source Law of large numbers, Wikipedia
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Source Law of large numbers, Wikipedia
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1. Law of large numbers, Wikipedia
Lead section
the law of large numbers is a mathematical law which states that the average of the results obtained from a large number of independent random samples converges to the true value, if it exists.
Lead
It took him over 20 years to develop a sufficiently rigorous mathematical proof which was published in his Ars Conjectandi (The Art of Conjecturing) in 1713.
In Branch: Probability and Statistics, Lead sentence
In probability theory, the law of large numbers is a mathematical law which states that the average of the results obtained from a
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