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Under standard independence and moment hypotheses, sample averages converge to the common expectation, in probability for the weak law and almost surely for the strong law.
Independence alone is insufficient; the precise weak or strong law and its integrability or variance hypotheses must be stated.
wp-law-large-numbersnlab-law-large-numbersdurrett-probabilityEach relation below ends at this concept.
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In the iid integrable case, the strong law gives almost-sure convergence of sample averages to the common mean; weaker variants use their own explicit assumptions.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
wp-law-large-numbersnlab-law-large-numbersdurrett-probabilityEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
The weak law asserts convergence in probability of sample averages to the relevant expectation under its stated hypotheses.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
wp-law-large-numberswp-convergence-random-variablesdurrett-probability