International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 10, Pages 663-673
doi:10.1155/S0161171200001757
Stability of a characterization of normal distributions based on the first two conditional moments
Truc T. Nguyen1
and Khoan T. Dinh2
1Department of Mathematics and Statistics, Bowling Green State University, Bowling Green 43403-0221, Ohio, USA
2Environmental Protection Agency, Washington 20460, DC, USA
Abstract
A characterization of normal distributions of two independent random variables X and Y with a finite E[X2] based on the linearity of E[X|X+Y] and the homoscedasticity of var[X|X+Y] given by Rao (1976) is proved to be stable.