aspg-33-2030-1792222842 20261017074042 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 2023 7 2 Mohamed Bisher Zeina Department of Mathematical Statistics, Faculty of Science, University of Aleppo, Aleppo, Syria Nizar Altounji Faculty of Science, Department of Mathematical Statistics, University of Aleppo, Aleppo, Syria Mohammad Abobala Department of Mathematics, Faculty of Science, Tishreen University, Latakia, Syria Yasin Karmouta Faculty of Science, Department of Mathematical Statistics, University of Aleppo, Aleppo, Syria 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. 2023 18 30 2030 https://creativecommons.org/licenses/by/4.0/ 10.54216/GJMSA.070202 https://americaspg.com/journal/33/article/2030 https://americaspg.com/storage/51693892441.pdf