2006/01/26 by Soumik Pal, Pal, Soumik
Mathematics · Physics and Astronomy · #60G99 #Advanced Mathematical Theories and Applications #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #History and Theory of Mathematics #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.math/0601652
openalex publication_date 2006/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a random variable. We shall call an independent random variable Y to be a symmetrizer for X, if X+Y is symmetric around zero. A random variable is said to be symmetry resistant if the variance of any symmetrizer Y, is never smaller than the variance of X itself. We prove that a Bernoulli(p) random variable is symmetry resistant if and only if p is not 1/2. This is an old problem proved in 1999 by Kagan, Mallows, Shepp, Vanderbei & Vardi using linear programming principles. We reprove it here using completely probabilistic tools using Skorokhod embedding and Ito's rule.