Abstract:
Properties of roots of generating functions of integer-valued bounded random variables and properties of sums of independent random variables with values in sets $\{0, 1\}$ and $\{0, 1, 2\}$ are studied. Conditions of weak convergence of integer-valued bounded random variables to the Poisson and normal laws in terms of roots of generating functions are presented.
Key words:integer-valued random variables, roots of probability generating functions, sums of independent simplest random variables, limit theorems.
Fulltext:
PDF file (471 kB)