Suppose that $X$ admits a second moment. Let $\delta$ be an element of $\mathbb{R}^{+*}$. Show that, for $n$ in $\mathbb{N}^{*}$, $$P\left(\left|S_{n} - nE(X)\right| \geqslant n\delta\right) \leqslant \frac{V(X)}{n\delta^{2}}$$
Suppose that $X$ admits a second moment. Let $\delta$ be an element of $\mathbb{R}^{+*}$. Show that, for $n$ in $\mathbb{N}^{*}$,
$$P\left(\left|S_{n} - nE(X)\right| \geqslant n\delta\right) \leqslant \frac{V(X)}{n\delta^{2}}$$