Suppose in this question that $X$ additionally admits a finite variance $V$. Show then that $$\forall \varepsilon > 0, \forall n \geqslant 1, \quad \mathbb{P}\left(S_n \leqslant n(m-\varepsilon)\right) \leqslant \frac{V}{\varepsilon^2 n}.$$
Suppose in this question that $X$ additionally admits a finite variance $V$. Show then that
$$\forall \varepsilon > 0, \forall n \geqslant 1, \quad \mathbb{P}\left(S_n \leqslant n(m-\varepsilon)\right) \leqslant \frac{V}{\varepsilon^2 n}.$$