Let \(X_{1}, \ldots, X_{n}\) be a set of independent and identically distributed random variables from a distribution \(F\) with \(E\left(\left|X_{1}ight|^{k}ight)<\infty\). Prove that \(\hat{\mu}_{k} \xrightarrow{\text { a.c. }} \mu_{k}\) as \(n ightarrow \infty\).