It was shown earlier by I. M. Lifshitz and two of us that the evolution of the relativistic cosmological models towards the singularity undergoes spontaneous stochastization.(1) In the present paper it is shown that the statistical parameters of this evolution can be calculated in an exact manner. From the point of view of the general ergodic theory we deal here with a specific mode of stochastization of a deterministic dynamical system with a five-dimensional phase space. The knowledge of the source of stochasticity makes it possible to develop a quantitative statistical theory with appreciable completeness.