LLN
E582381
LLN is a fundamental theorem in probability theory stating that as the number of independent, identically distributed trials increases, the sample average converges to the expected value.
All labels observed (1)
| Label | Occurrences |
|---|---|
| LLN canonical | 1 |
Statements (38)
| Predicate | Object |
|---|---|
| instanceOf |
law of large numbers
ⓘ
probability theorem ⓘ |
| alsoKnownAs |
strong law of large numbers
ⓘ
weak law of large numbers ⓘ |
| appliesTo | independent identically distributed random variables ⓘ |
| assumes |
finite expected value
ⓘ
identical distribution of trials ⓘ independence of trials ⓘ |
| category | limit theorem in probability ⓘ |
| contrastedWith | central limit theorem NERFINISHED ⓘ |
| describes | convergence of sample averages to expected value ⓘ |
| ensures | stability of long-run frequencies ⓘ |
| field |
probability theory
ⓘ
statistics ⓘ |
| formalization | measure-theoretic probability framework ⓘ |
| formalizes | long-run average behavior of random experiments ⓘ |
| fullName | law of large numbers NERFINISHED ⓘ |
| hasConsequence | empirical mean is consistent estimator of expectation ⓘ |
| hasVariant |
strong law of large numbers
ⓘ
weak law of large numbers NERFINISHED ⓘ |
| historicalOrigin | Jakob Bernoulli NERFINISHED ⓘ |
| holdsUnder | certain moment conditions ⓘ |
| implies |
law of averages in colloquial terms
ⓘ
sample mean approximates population mean ⓘ |
| mathematicalObject | theorem about sequences of random variables ⓘ |
| motivates | use of sample averages in statistics ⓘ |
| provenBy |
Chebyshev
NERFINISHED
ⓘ
Kolmogorov NERFINISHED ⓘ |
| relatedConcept |
Borel–Cantelli lemma
NERFINISHED
ⓘ
Chebyshev inequality NERFINISHED ⓘ ergodic theorem ⓘ |
| requires | large number of trials ⓘ |
| typeOfConvergence |
almost sure convergence
ⓘ
convergence in probability ⓘ |
| usedIn |
Monte Carlo methods
ⓘ
frequentist interpretation of probability ⓘ statistical inference ⓘ |
| yearFirstFormulated | early 18th century ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.