Asymptotic States of the Sum of Random Variables - Rakhimova Shokhsanam (Genius Journals, 2022)
Most of the problems of probability theory are connected with the study of sums of random variables. The distribution of the sum of independent random variables is determined by the composition of the distributions of each additive. But this operation, defined in the class of distribution functions, is complicated, and in connection with this, efforts aimed at accurately calculating the distribution of the sum of random variables turn out to be useless. Therefore, problems of approximating the distribution of the sum of random variables with the help of asymptotic expressions are of great importance. In turn, the problems of approximation of distributions are connected with the limit theorems of probability theory
Keywords: Probability theory; sequence of random variables; central limit theorem; Lindeberg condition