  Two-phase composites with non-overlapping inclusions randomly embedded in
matrix are investigated. A straight forward approach is applied to estimate the
effective properties of random 2D composites. First, deterministic boundary
value problems are solved for all locations of inclusions, i.e., for all events
of the considered probabilistic space $\mathcal C$ by the generalized method of
Schwarz. Second, the effective properties are calculated in analytical form and
averaged over $\mathcal C$. This method is related to the classic method based
on the average probabilistic values involving the $n$-point correlation
functions. However, we avoid computation of the correlation functions and
compute their weighted moments of high orders by an indirect method which does
not address to the correlation functions. The effective properties are exactly
expressed through these moments. It is proved that the generalized method of
Schwarz converges for an arbitrary multiply connected doubly periodic domain
and for an arbitrary contrast parameter. The proposed method yields effective
in symbolic-numeric computations formulae of high order in concentration. In
particular, the Torquato--Milton parameter $\zeta_1$ is exactly written for
circular inclusions.
