Bienaymé–Chebyshev inequality
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:inequality
|
| gptkbp:appliesTo |
random variables
|
| gptkbp:category |
inequality (mathematics)
probability inequality |
| gptkbp:field |
gptkb:probability_theory
|
| gptkbp:generalizes |
gptkb:Markov's_inequality
|
| https://www.w3.org/2000/01/rdf-schema#label |
Bienaymé–Chebyshev inequality
|
| gptkbp:introducedIn |
1867
|
| gptkbp:namedAfter |
gptkb:Pafnuty_Chebyshev
gptkb:Irénée-Jules_Bienaymé |
| gptkbp:publishedIn |
gptkb:Journal_de_Mathématiques_Pures_et_Appliquées
|
| gptkbp:state |
For any real-valued random variable X with finite expected value μ and finite non-zero variance σ², and for any real number k > 0, P(|X − μ| ≥ kσ) ≤ 1/k².
|
| gptkbp:usedFor |
bounding tail probabilities
proving laws of large numbers |
| gptkbp:bfsParent |
gptkb:Chebyshev's_inequality
gptkb:Chebyshev's_theorem gptkb:Chebyshev_inequality |
| gptkbp:bfsLayer |
7
|