Year: 2025
Type: article
Abstract: In an article in this journal, Kanellopoulos, Razis, and van der Weele provided a key formula that describes the evolution of the cumulative distribution of the Persian Immortals' fighting abilities during a battle where fallen soldiers, who are more likely to be weaker than average, are replaced by reserve soldiers with average strength. They also calculated the limit distribution, which shows the final strength advantage of the fighting army over the reserve unit. However, their arguments to derive the mentioned key formula may be difficult to follow for some readers who are not familiar with how the cumulative distribution function of a set changes when some of its elements are replaced. Here, we present a simpler yet more general method to derive this formula. This makes Kanellopoulos, Razis, and van der Weele's compelling exercise more appropriate for an introductory undergraduate course.
Source: American Journal of Physics
DOI: 10.1119/5.0237521
Author: Santos Bravo Yuste
Institution: Universidad de Extremadura
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Award: G6351825672
OpenAlex ID: W4407760686