  In this paper we prove a sharp Ostrowski type inequality for random processes
of certain classes. This inequality is later applied to a solution of the
optimal recovery of the integral $\int_0^1\xi_tdt$, using the random variables
$\xi_{\tau_1},\dots, \xi_{\tau_n}$ as an information set, where $\tau_1,\dots,
\tau_n$ are random variables. We also consider the problem of the information
set optimization.
