Sharp bounds on moments of random variables

Author:

Caraballo David

Abstract

AbstractWe give new inequalities involving the expectation and variance of a random variable defined on a finite interval and having an essentially bounded probability density function. Our inequalities sharpen previous inequalities by N.S. Barnett and S.S. Dragomir. We prove our bounds are optimal, and we explicitly give the cases in which equality occurs.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Reference8 articles.

1. Agarwal, R.P., Barnett, N.S., Cerone, P., Dragomir, S.S.: A survey on some inequalities for expectation and variance. Comput. Math. Appl. 49, 429–480 (2005)

2. Barnett, N.S., Cerone, P., Dragomir, S.S.: Further inequalities for the expectation and variance of a random variable defined on a finite interval. Math. Inequal. Appl. 6(1) (2000)

3. RGMIA Monographs,2004

4. Barnett, N.S., Cerone, P., Dragomir, S.S., Roumeliotis, J.: Some inequalities for the dispersion of a random variable whose pdf is defined on a finite interval. J. Inequal. Pure Appl. Math. 2(1), Art. 1 (2001)

5. Barnett, N.S., Dragomir, S.S.: Some elementary inequalities for the expectation and variance of a random variable whose pdf is defined on a finite interval. RGMIA Res. Rep. Collect. 2(7), Art. 12 (1999)

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