It is well known that many practical optimization problems with random elements lead from the mathematical point of view to deterministic optimization problems depending on the random elements through probability laws only. Further, it is also well known that these probability laws are known very seldom. Consequently, statistical estimates of the unknown probability measure, if they exist, must be employed to obtain some estimates of the optimal value and the optimal solution, at least.

If the theoretical distribution function is completely unknown then an empirical distribution usually substitutes it [2, 3, 9, 17, 31]. The great attention has been already paid to the studying of statistical properties of such arised empirical estimates, in the literature. We can remember here the works [4, 5, 6, 10, 13, 16, 32], for example. The aim of this paper is to discuss the convergence rate. For this we shall employed the assertions of the papers [10, 11, 13].