The Cube of a Normal Distribution is Indeterminate

Abstract

It is established that if X X is a stochastic variable with a normal distribution, then X2n+1 X 2 n + 1 has an indeterminate distribution for n≥1 n ≥ 1 . Furthermore, the distribution of |X|α | X | α is determinate for 0 < α ≤ 4 while indeterminate for α>4 α > 4 .