Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Bienaymé–Chebyshev_inequality
|
| gptkbp:appliesTo |
random variables with finite mean and variance
|
| gptkbp:describes |
probability of deviation from mean
|
| gptkbp:field |
gptkb:probability_theory
statistics |
| gptkbp:generalizes |
gptkb:Markov's_inequality
|
| https://www.w3.org/2000/01/rdf-schema#label |
Chebyshev's inequality
|
| gptkbp:isNonparametric |
true
|
| gptkbp:namedAfter |
gptkb:Pafnuty_Chebyshev
|
| gptkbp:publishedIn |
gptkb:Journal_de_Mathématiques_Pures_et_Appliquées
|
| gptkbp:satisfies |
all probability distributions with finite variance
|
| gptkbp:state |
For any real number k > 0, the probability that the value of a random variable differs from its mean by more than k standard deviations is at most 1/k^2.
|
| gptkbp:usedFor |
bounding tail probabilities
|
| gptkbp:yearProposed |
1867
|
| gptkbp:bfsParent |
gptkb:Probability_theory
gptkb:Markov's_inequality |
| gptkbp:bfsLayer |
6
|