On inequalities of the Tchebychev type
- 1 January 1963
- journal article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 59 (1) , 135-146
- https://doi.org/10.1017/s0305004100002085
Abstract
1. A type of problem which frequently occurs in probability theory and statistics can be formulated in the following way. We are given real-valued functionsf(x),gi(x) (i= 1, 2, …,k) on a space(typically finite-dimensional Euclidean space). Then the problem is to set bounds for Ef(X), whereXis a random variable taking values in, about which all we know is the values of Egi(X). For example, we might wish to set bounds for P(X>a), whereXis a real random variable with some of its moments given.This publication has 7 references indexed in Scilit:
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- A MULTIVARIATE GENERALIZATION OF TCHEBICHEV'S INEQUALITYThe Quarterly Journal of Mathematics, 1958
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- On the Tchebychef Inequality of BernsteinThe Annals of Mathematical Statistics, 1933