Probabilistic Ostrowski type inequalities

New very general univariate and multivariate probabilistic Ostrowski type inequalities are established, involving ∥·∥∞ and ∥·∥p, p ≥ 1 norms of probability density functions. Some of these inequalities provide pointwise estimates to the error of probability distribution function from the expectation of some simple function of the engaged random variable. Other inequalities give upper bounds for the expectation and variance of a random variable. All are done over finite domains. At the end are given applications, especially for the Beta random variable