Let $\{ X_n, n\geq 1 \}$ be a sequence of independent random variables with
$P(X_n=n^{\lambda})=P(X_n=-n^{\lambda})=\frac{1}{2}$ where $0<\lambda<\infty$
Show that the central limit theorem is applicable to this sequence.
I calculate the $E(X_n)=0$, $Var(X_n)=n^{2\lambda}$, but I really don't understand the question, How so I show the "applicable"?
Check if Lindeberg's condition holds for your sequence. If it is satisfied, then the CLT applies.