Symmetrization of Bernoulli
| dc.creator | Pal, Soumik | |
| dc.date | 2006-01-26 | |
| dc.date.accessioned | 2026-07-07T06:59:20Z | |
| dc.date.available | 2026-07-07T06:59:20Z | |
| dc.description | 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. | |
| dc.description | 3 pages; a completely probabilistic proof of a theorem due to Kagan, Mallows, Shepp, Vanderbei & Vardi | |
| dc.identifier | https://arxiv.org/abs/math/0601652 | |
| dc.identifier | http://arxiv.org/abs/math/0601652 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107712 | |
| dc.subject | Probability | |
| dc.subject | 60G99 | |
| dc.title | Symmetrization of Bernoulli | |
| dc.type | text |