Introduction to Symbolic 2-Plithogenic Probability Theory
Mohamed Bisher Zeina*1, Nizar Altounji2, Mohammad Abobala3, Yasin Karmouta4
1 Department of Mathematical Statistics, Faculty of Science, University of Aleppo, Aleppo, Syria
2 Faculty of Science, Department of Mathematical Statistics, University of Aleppo, Aleppo, Syria
3 Department of Mathematics, Faculty of Science, Tishreen University, Latakia, Syria
4 Faculty of Science, Department of Mathematical Statistics, University of Aleppo, Aleppo, Syria
Emails: bisher.zeina@gmail.com ; nizar.altounji.94@hotmail.com; mohammadabobala777gmail.com ; yassinkarmouta@gmail.com
Abstract
In this paper we present for the first time the concept of symbolic plithogenic random variables and study its properties including expected value and variance. We build the plithogenic formal form of two important distributions that are exponential and uniform distributions. We find its probability density function and cumulative distribution function in its plithogenic form. We also derived its expected values and variance and the formulas of its random numbers generating. We finally present the fundamental form of plithogenic probability density and cumulative distribution functions. All the theorems were proved depending on algebraic approach using isomorphisms. This paper can be considered the base of symbolic plithogenic probability theory.
Keywords: Plithogenic; Probability Density Function; Cumulative Distribution Function; Random Numbers Generation; Exponential Distribution; Uniform Distribution.