The Distribution Function of Random Variable and Extension of Mathematical Expectation

Abstract This work reveals the existence of non-discrete and non-continuous random variables and discusses specific characteristics of the distribution functions of discrete and continuous random variables. It is constructed to create a class of single random variables that are neither discrete nor continuous. Their distribution functions are compared with those of continuous and discrete random variables. Its qualities are then spoken about. To evaluate the discontinuous points of these random variables, an example is provided. We also examine the process of computing the mathematical expectation of a certain type of random variable that is associated with the distribution function that has countable discontinuous points. Examples and applications are also given to make illustrations. And through the national Postgraduate Admission Test questions on the above issues were explained.