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gptkbp:instanceOf
|
statistical theorem
|
|
gptkbp:alsoKnownAs
|
gptkb:LLN
|
|
gptkbp:appliesTo
|
independent and identically distributed random variables
|
|
gptkbp:category
|
probability theorems
statistical laws
|
|
gptkbp:describes
|
convergence of sample averages to expected value
|
|
gptkbp:field
|
gptkb:probability_theory
|
|
gptkbp:formedBy
|
gptkb:Jacob_Bernoulli
1713
|
|
gptkbp:generalizes
|
gptkb:Kolmogorov's_strong_law
|
|
gptkbp:hasVersion
|
gptkb:strong_law_of_large_numbers
gptkb:weak_law_of_large_numbers
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
law of large numbers
|
|
gptkbp:implies
|
sample mean converges to population mean
|
|
gptkbp:mathematicalStatement
|
For any ε > 0, P(|X̄_n - μ| > ε) → 0 as n → ∞
|
|
gptkbp:publishedIn
|
gptkb:Ars_Conjectandi
|
|
gptkbp:relatedTo
|
gptkb:ergodic_theorem
gptkb:central_limit_theorem
|
|
gptkbp:usedIn
|
economics
finance
statistics
actuarial science
|
|
gptkbp:bfsParent
|
gptkb:Monte_Carlo_method
gptkb:Theory_of_Probability
gptkb:asymptotic_equipartition_property
gptkb:probability_theory
gptkb:Monte_Carlo_methods
|
|
gptkbp:bfsLayer
|
5
|