Real life applications of mathematical model of Kifilideen trinomial theorem distribution of positive powers of <i>n</i> with mathematical induction of the constituents of its negative powers of <i>n</i> counterpart

Abstract

Binomial system is a system of analysis which involves two chances or possible outcomes of event which are the extreme ends of such event. In real life, there exist the mid or intermediary chances or possible outcomes of some events, if not all events, making the possible outcomes of such events to be three. In any such scenario or instance of three possible outcomes, a trinomial system of analysis would be applicable. There is need to develop a model to analysis such scenarios of trinomial system. This research work presents real life applications of mathematical model of Kifilideen trinomial theorem distribution of positive powers of n with mathematical induction of negative powers of n counterpart. A mathematical model of the Kifilideen trinomial theorem distribution was formulated. This research work also develops alternate Kifilideen power combination formula, alternate Kifilideen term formula and alternate Kifilideen position formula for the negative powers of n, which conform but not the same, with the one developed for the positive powers of n counterpart. The formulated mathematical model of the Kifilideen trinomial theorem distribution was utilized to analysis real life events having three possible outcomes. The model invented in this paper can be used to determine the probability of the combination of different n outputs involving three possible categories of outcomes of events. The mathematical induction helps to support and prove that the developed Kifilideen formulas for the constituents of Kifilideen trinomial theorem of negative powers of n are valid and true.