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Exact Modes and Antimodes of Two-Term Weighted Sums of Discrete Uniform Random Variables

Year: 2026

Type: preprint

Abstract: This paper studies the weighted sum Z=aX+bY, where X and Y are independent discrete uniform random variables. The modes and antimodes of Z are determined by counting lattice points. When N=b, the antimodes are exactly the values with a unique representation. Their number is also obtained and eventually becomes 2ab.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.22026237

Author: Hu, Po

Language: English

Topic: Probability and Statistical Research

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7203923524

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