Probability Inequalities Related to Markov's Theorem
- 1 August 2002
- journal article
- Published by Taylor & Francis in The American Statistician
- Vol. 56 (3) , 186-190
- https://doi.org/10.1198/000313002119
Abstract
A recurrent theme of interest in probability and statistics is to determine the best bounds for two probabilities, Pr(X ≥ r) and Pr(s < X - μ < t), when only the mean μ and the standard deviation σ of a random variable X are known. This article addresses the issue under two circumstances, when X is arbitrary and when X is nonnegative. The answers are provided in a unified manner using only Markov's theorem. The existing literature on related inequalities is reviewed. Some examples are given to illustrate the use of the inequalities.Keywords
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