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Theorem

Law of Large Numbers

Probability and Statistics

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.

Facts
Statement
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. 1
Classification
Statement Form
Characterization Theorem 1
Connections

Has Statement Form

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

In Branch

Source Law of large numbers, Wikipedia
Sources
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.
  • 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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