Arnold, Barry C.; Isaacson, Dean L. - In: Stochastic Processes and their Applications 7 (1978) 2, pp. 227-230
If X1 and X2 are independent and identically distributed (i. i. d.) with finite variance, then (X1+X2)/[radical sign]2 has the same distribution as X1 if and only if X1 is normal with mean zero (Pólya [9]). The idea of using linear combinations of i. i. d. random variables to characterize the...
