General Mathematics

    

A Novel Identity in Binomial Probability Theory

Authors: Ashkan Karimi

This paper presents a proof and analysis of a previously unexploredbinomial probability identity involving weighted sums of binomial probabilities. The identity establishes that a specific weighted sum of binomial terms with probability parameter PA equals zero for any positive integer n. I provide a rigorous proof of this identity, explore its probabilistic interpretation in terms of expected values, and discuss potential applications in statistical analysis, information theory, and computational probability. The result offers new insights into the properties of binomial distributions and contributes to the broader understanding of discrete probability structures. The identity has particularly elegant connections to moment-generating functions and can be generalized to higher moments and other probability distributions.

Comments: 6 Pages.

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Submission history

[v1] 2025-03-14 18:56:27

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