Stability of a characterization of normal distributions based on the first two conditional moments
Truc T. Nguyen1and Khoan T. Dinh2
Received23 Mar 1998
Revised27 Jul 1998
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.