On some inequalities for the expectation and variance
type: Item
instance of: scholarly article
zbMATH Open document ID: 0983.26011
author: P. Cerone
author: Silvestru Sever Dragomir
publication date: 2002-04-16T00:00:00Z
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 1625580
zbMATH Keywords: expectation
zbMATH Keywords: variation
zbMATH Keywords: inequalities
MaRDI profile type: Publication
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title: On some inequalities for the expectation and variance
published in: The Korean Journal of Computational \& Applied Mathematics
review text: Let \(f:[a,b]\rightarrow\mathbb{R}\) be the p.d.f. of the random variable \(T\) and \(M_{n}=\int_{a}^{b}t^{n}f(t) dt\) be the moment of order \(n\) of \(T\). As usual, \(E(T)=M_{1}\) denotes the expectation of \(T\) and \(\sigma ^{2}(T)=M_{2}-M_{1}^{2}\) \ its variance. The authors obtain a variety of identities and bounds of the expression \(\sigma ^{2}(T)+[E(T)-\alpha ][E(T)-\beta ]\) , where \(\alpha ,\beta \in [a,b]\) .
reviewed by: Gheorghe Toader
description: scientific article; zbMATH DE number 1625580