I'm looking for the proof of the following theorem/statement.
$$
\begin{align}
\lim_{n \to \infty} M_{X_n}(t) = M_X(t)
\end{align}
$$
for every fixed [itex]t \in \mathbb{R}[/itex].
My book only states the theorem without proving it and I haven't found a proof online. Any help is appreciated! :)
$$
\begin{align}
\lim_{n \to \infty} M_{X_n}(t) = M_X(t)
\end{align}
$$
for every fixed [itex]t \in \mathbb{R}[/itex].
My book only states the theorem without proving it and I haven't found a proof online. Any help is appreciated! :)
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