An expands Definition the Random Variable in Probability Theory

Abstract

This paper clarifies how to deal with the random variable expands its definition, and recognizes the statistical measures of random processes, such as prediction and variance in a more appropriate form for random processes, to work on the random variable and link these processes to real processes through a real function "The density function". It also focuses on discussing the characteristics of the statistical independence of the random variable and the ability to work on it in terms of new definitions. Then clarify the idea of a random convergence to a random variable using "BOREL-CONTELLI LEMMA" to work on the stochastic differential equations.