Hoeffding inequality
= Hoeffding inequality
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If independent random variables satisfy $a_i\leq X_i\leq b_i$, then
$$
\mathbb P\left(\sum_i(X_i-\mathbb EX_i)\geq t\right)
\leq\exp\left(-\frac{2t^2}{\sum_i(b_i-a_i)^2}\right),
$$
with the same bound for the lower tail.