Statements (13)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:inequality
|
| gptkbp:appliesTo |
sequence of independent random variables
|
| gptkbp:field |
gptkb:probability_theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Kolmogorov's inequality
|
| gptkbp:namedAfter |
gptkb:Andrey_Kolmogorov
|
| gptkbp:publishedIn |
1930s
|
| gptkbp:relatedTo |
gptkb:Kolmogorov's_strong_law_of_large_numbers
|
| gptkbp:sentence |
For independent mean-zero random variables X_1,...,X_n with finite variances, for any λ>0, P(max_{1≤k≤n} |S_k| ≥ λ) ≤ (1/λ^2) Var(S_n), where S_k = X_1+...+X_k.
|
| gptkbp:type |
maximal inequality
|
| gptkbp:usedFor |
bounding probability of large deviations
|
| gptkbp:bfsParent |
gptkb:Andrey_Kolmogorov
gptkb:Andrei_Kolmogorov |
| gptkbp:bfsLayer |
5
|