Email this article A conditional version of Chebyshev’s other inequality
- Authors: Golikova N.1,2, Kruglov V.1,2
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Affiliations:
- Faculty of Physics and Mathematics
- Department of Statistics, Faculty of Computational Mathematics and Cybernetics
- Issue: Vol 37, No 4 (2016)
- Pages: 404-408
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/197998
- DOI: https://doi.org/10.1134/S1995080216040077
- ID: 197998
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Abstract
Under the conditions of integrability the conditional version E(f(X)G)E(g(X)|G) ≤ E(f(X)g(X)|G) a.s. of Chebyshev’s other inequality is proved for monotonic functions f and g of the samemonotonicity, for any random variable X, and for any σ-algebra G. An improved conditional version of the Grüss inequality is also proved.
About the authors
N. Golikova
Faculty of Physics and Mathematics; Department of Statistics, Faculty of Computational Mathematics and Cybernetics
Author for correspondence.
Email: nina.golikova@mail.ru
Russian Federation, ul. Radio 10A, Moscow, 105005; Moscow, 119992
V. Kruglov
Faculty of Physics and Mathematics; Department of Statistics, Faculty of Computational Mathematics and Cybernetics
Email: nina.golikova@mail.ru
Russian Federation, ul. Radio 10A, Moscow, 105005; Moscow, 119992
