Abstract
In this paper, some Grüss and Ostrowski–Grüss type inequalities are applied to estimate the moments of continuous random variables whose probability density function is in L p -space. Some results of Kumar are generalized [P. Kumar, Inequalities involving moments of a continuous random variable defined over a finite interval, Comput. Math. Appl. 48 (2004) 257–273; P. Kumar, The Ostrowski type moment integral inequalities and moment-bounds for continuous random variables, Comput. Math. Appl. 49 (2005) 1929–1940].
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