Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
statistical theorem
|
| gptkbp:alsoKnownAs |
gptkb:Chebyshev's_inequality
|
| gptkbp:appliesTo |
random variables with finite mean and variance
all probability distributions |
| gptkbp:category |
Inequalities in probability theory
Theorems in statistics |
| gptkbp:compatibleWith |
gptkb:normal_distribution
|
| gptkbp:generalizes |
gptkb:Bienaymé–Chebyshev_inequality
|
| https://www.w3.org/2000/01/rdf-schema#label |
Chebyshev's theorem
|
| gptkbp:namedAfter |
gptkb:Pafnuty_Chebyshev
|
| gptkbp:provides |
bound on probability of deviation from mean
|
| gptkbp:publishedIn |
19th century
|
| gptkbp:state |
For any real number k > 1, at least 1 - 1/k^2 of the distribution's values lie within k standard deviations of the mean
|
| gptkbp:usedIn |
gptkb:probability_theory
statistics |
| gptkbp:bfsParent |
gptkb:Pafnuty_Chebyshev
gptkb:Prime_Number_Theorem |
| gptkbp:bfsLayer |
6
|