CHARACTERISTIC FUNCTIONS OF RANDOM VARIABLES AND THEIR PROPERTIES

Abstract

In probability theory, methods and analytical apparatus from various branches of mathematical analysis are widely used. Simple solutions to many problems encountered in probability theory, especially those involving sums of uncorrelated random variables, can be found using characteristic functions, developed in mathematical analysis and known as Fourier transforms. The fact that the method of characteristic functions is one of the main tools of the analytical apparatus of probability theory can be clearly seen in the proof of limit theorems, in particular, in the proof of the central limit theorem, which generalizes the Moivre-Laplace theorem. In this article, we will limit ourselves to describing the main properties of characteristic functions.