[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Find a sequence of uniformly bounded discrete independent random

variables [math]\{X_n\}[/math] such that the variance of their sum does not tend to [math]\infty[/math] as [math]n \rightarrow \infty[/math], and such that their sum is not asymptotically normally distributed.