Problem 12.6 (Optional: Strong Law of Large Number). Let $X_1, X_2, \dots$ be a iid random sequence with $E[X_i] = 0$, $E[X_i^2] = \sigma^2$, and $E[|X_i|^4] < \infty$. Consider the sample mean \begin{equation*} \overline{X}_n := \frac{1}{n} \sum_{i=1}^n X_i. \end{equation*} (i) Show that $\overline{X}_n \stackrel{a.s.}{\rightarrow} 0$. Hint: You may use the fact that $E[\overline{X}_n^4] = \frac{n\gamma + 3n(n-1)\sigma^4}{n^4}$.