ON THREE CHARACTERIZATIONS OF THE NORMAL DISTRIBUTION

Abstract: Of all the characterizations of the normal distribution, three landmarks are the
theorems of Bernstein and Skitovitch concerning independence of linear forms and the
theorem of Geary concerning independence of sample mean and variance. In this
note, ideas from several proofs of these theorems are distilled to give unified proofs
which depend mostly on simple probability and characteristic function concepts.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -