On computer verstions of statistical procedures

This paper contains a discription and a partial decision of problems connected with computer realization of statistical procedures. The main problem under consideration is the analysis of the influence of rounding operations on computer process when the number of observations is very large ($10^8 -- 10^{10}$) . It is shown that the fundamental asymptotic theorems such as the law of large numbers and the lentral limit theorem cease to be true when “ideal” addition and norming are replaced by their rounding analogues.