In this paper, we consider the class of normalized analytic functions of the form $f(z)=z+\sum_{n=2}^\infty a_nz^n$. Following this functions, we define the functions whose coefficients are probabilities of the geometric distribution series and other special modes of this series. Also, we consider different special classes of $f(z)$. In the following we consider some lemmas that make connection between defined special classes with the function $f(z)$. Follower of this topic we will consider the theorems that make connection between defined classes with the functions whose coefficients are probabilities of geometric distribution series. Also we define Alexander-type integral operator and find the necessary and sufficient conditions for being this operator to defined general classes.
