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December, 1972 A Note on Symmetric Random Variables
David L. Burdick
Ann. Math. Statist. 43(6): 2039-2040 (December, 1972). DOI: 10.1214/aoms/1177690880


There exist independent random variables $X_1$ and $X_2$ such that $X_1$ is symmetric, $X_2$ is not symmetric, but $X_1 + X_2$ is symmetric. If $X_1$ and $X_2$ are i.i.d. random variables with a fractional moment and if for all real $\alpha P\lbrack X_1 + \alpha X_2 > 0\rbrack = \frac{1}{2}$ then they are symmetric.


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David L. Burdick. "A Note on Symmetric Random Variables." Ann. Math. Statist. 43 (6) 2039 - 2040, December, 1972.


Published: December, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0248.60011
MathSciNet: MR353415
Digital Object Identifier: 10.1214/aoms/1177690880

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 6 • December, 1972
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