ON THE ROLE OF BERNOULLI DISTRIBUTION IN COSMOLOGY

Cosmological observations suggest that the transition scale to homogen eity is not smaller than similar or equal to(200-300)h(-1) Mpc (h is t he Hubble parameter in units 100 km s(-1) Mpc(-1)), and that - in addi tion - this transition scale seems to decrease with increasing redshif t. Nevertheless, these claims are highly uncertain, and call for furth er observational tests allowing to verify the homogeneity even on scal es similar or equal to(400-1000)h(-1) Mpc for different redshifts. The key ideas of such a test are presented. Simultaneous pencil beam surv eys are proposed to be done, and then the randomness of observed objec ts should be verified by the so called ''Bernoulli test''. The method is in fact a generalization of the usual counts-in-cells analysis, whe re the Poisson distribution is substituted by the Bernoulli distributi on. Hence, it is shown that this distribution may have a great importa nce in cosmology.