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Author(s): Njoku K. C. N., Okoli O. C..

Volume/Issue: Volume 7 , Issue 3 (2024)

Abstract:

Let u,v∈N(u<v) and {T(x,y)=p^x q^y:x,y=u,u+1,u+2,u+3,…,v} be a string of sequence of success-failure events constituting the Bernoulli trials, with success p and failure q. Several probability distributions have derived it root from the sequences of this form. However, it is our purpose to introduce a new probability distribution functions that unify some of the existing once generated by sets of this form mentioned in the literature and then give some of the statistics associated with it.

Keywords:

Probability mass function, geometric random variable, independent identically distributed (iid) random variable, moments, binomial expansion.

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