The Department of Mathematics and Statistics at the Faculty of Natural and Applied Sciences – Shouf Campus hosted a lecture entitled “The Complex Probability Paradigm and Stochastic Distributions.” The lecture was delivered by Dr. Abdo Abou Jaoude on Monday, November 28, 2016. Dr. Abou Jaoude discussed before Maths and Engineering students his latest findings that would help develop further the new field of the Complex Probability Paradigm.
Dr. Abdo Abou Jaoude took the floor to explain the five basic axioms of Andrey N. Kolmogorov, which define the probability in the real set R and do not take into consideration the imaginary part M which takes place in the complex set C = R + M, a problem that we are facing in applied and pure mathematics. Dr. Abou Jaoude added that whatever the probability distribution of the random variable in R is, the corresponding probability in the whole set C is always equal to one, so the outcome of the random experiment in C can be predicted totally and perfectly. This is the consequence of the fact that the probability in C is got by subtracting the chaotic factor from the degree of our knowledge of the system. He also defined the complex random vectors and their resultant complex random vector Z that represents the whole distribution and system in the complex plane C. And also defined the imaginary and the complex expectations and variances and proved the law of large numbers in a new way using Z.
The concept of the complex random vector became clear, evident, and it follows directly from the newly added axioms. This result was elaborated throughout this lecture using nine discrete and continuous stochastic distributions. In addition, this lecture developed more the new field of the “Complex Probability Paradigm” that considers all the random variables in the complex set C. Thus, the law of large numbers proves that this complex extension is successful and fruitful.
Students appreciated Dr. Abou Jaoude’s contributions to the new field and expressed much interest in learning about the field.