Reading Roch's Modern Discrete Probability one finds the following exercise (2.6):
(Sums of uncorrelated variables). Centered random variables $X_1,\dots X_n$ are uncorrelated if forr all $r$ and for all $s$, if $r\neq s$, then $\mathbb{E}[X_r X_s] = 0$. Assume that $Var[X_r]\leq X \leq \infty$ for all $r$. Show that
$$ \mathbb{P}\left(\frac{1}{n}\sum_{r\leq n}{X_r}\geq \beta\right) \leq \frac{C^{2}}{\beta^{2}n} $$
By using the fact that for all $x$, $x\leq |x|$, Chebyshev's inequality and the fact that the random variables are not correlated we can get to the desired result except for the square of $C$. I am wondering if the book has a typo or if we can indeed get the exact bound proposed by Roch.