New bounds for moments of continuous random variables

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 LpLp-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].