Year: 2025
Type: article
Abstract: If four people with Gaussian‐distributed heights stand at Gaussian positions on the plane, the probability that there are exactly two people whose height is above the average of the four is exactly the same as the probability that they stand in convex position; both probabilities are . We show that this is a special case of a more general phenomenon: The problem of determining the position of the mean among the order statistics of Gaussian random points on the real line (Youden's demon problem) is the same as a natural generalization of Sylvester's four point problem to Gaussian points in . Our main tool is the observation that the Gale dual of independent samples in itself can be taken to be a set of independent points (translated to have barycenter at the origin) when the distribution of the points is Gaussian.
Source: Mathematika
DOI: 10.1112/mtk.70015
Authors: Florian Frick, Andrew Newman, Wesley Pegden
Institution: Carnegie Mellon University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: National Science Foundation
OpenAlex ID: W4407673434