Math 6010 • Linear Models

Let \(X_1,X_2,\ldots\) be i.i.d. mean 0, variance 1 random variables
and \(S_n=X_1+\cdots+X_n\) for each \(n\geq1\). Show directly that the
characteristic function of \(S_n/\sqrt{n}\) converges pointwise to the
characteristic function of the standard normal distribution. Notice that this is
a key step in the proof of the central limit theorem, so you are \emph{not}
allowed to use the central limit theorem in your derivation.