The Faculty of Natural and Applied Sciences, Department of Mathematics and Statistics at Notre Dame University-Shouf Campus, organized a lecture under the title of “The Complex Probability Paradigm and Chebyshev’s Inequality”, which was held on Friday, May 5th, 2017, in the conference room, and presented by Dr. Abdo Abou Jaoudé.
Dr. Abdo Abou Jaoudé took the floor to explain the system of axioms for probability theory which were laid in 1933 by Andrey Nikolaevich Kolmogorov and that can be extended to encompass the imaginary set of numbers by adding to Kolmogorov’s original five axioms an additional three axioms. Therefore, we create the complex probability set C, which is the sum of the real set R with its corresponding real probability, and the imaginary set M with its corresponding imaginary probability. Hence, all stochastic experiments are performed now in the complex set C instead of the real set R.
Dr. Abou Jaoudé explained that the objective is then to evaluate the complex probabilities by considering supplementary new imaginary dimensions to the event occurring in the ‘real’ laboratory. Consequently, the corresponding probability in the whole set C is always equal to one and the outcome of the random experiments that follow any probability distribution in R is now predicted totally in C. Subsequently, it follows that, chance and luck in R is replaced by total determinism in C. Thus, by subtracting the chaotic factor from the degree of our knowledge of the stochastic system, we evaluate the probability of any random phenomenon in C. Dr. Abou Jaoudé added that this novel complex probability paradigm will be applied to the established theorem of Pafnuty Chebyshev’s inequality and to extend the concepts of expectation and variance to the complex probability set C.
In addition, Dr. Abou Jaoudé showed in this lecture how he developed the new field of the “Complex Probability Paradigm” created by him and that considers all the random variables in the complex set C. Accordingly, the application to Chebyshev’s inequality proves that this complex extension is both successful and fruitful.