Definite Probabilities from Division of Zero by Itself Perspective

Abstract

Over the years, the issues surrounding the division of zero by itself remained a mystery until year 2018 when the mystery was solved in numerous ways. Afterwards, the same solutions provided opened many other doors in academic space and one of the applications is in sure probabilities. This research is all about the sure probabilities computed from the zero divided by itself point of view. The solutions obtained in the computations are in harmony with logic and basic knowledge. A wide range of already existing probability distribution functions has been applied in different scenarios to compute the sure probabilities unanimously and new findings have also been encountered along the way. Some of the discrete and continuous probability distribution functions involved are the binomial, hypergeometric, negative binomial, Poisson, normal and exponential among others. It has been found in this work that sure probabilities can be evaluated from the division of zero by itself perspective. Another new finding is that in case of combinatorial, if the numerator is smaller than the denominator, then the solutions tend to zero when knowledge in gamma functions, integrations and factorials is applied. Again, if the case of continuous pdf involves integration and random variable specified in the direction of the parameter, then indirect computation of such probabilities should be applied. Finally, it has been found that the expansion of the domains of some of the parameters in some existing probability distribution functions can be considered and the restriction in conditional probabilities can be revised.