Hoeffding inequality

Theorem

Let $X_1,X_2,...,X_k$ be independent random variables with each $X_i \in [a_i,b_i]$. Let $\mu_i=\mathbb{E}[X_i]$ and $\mu=\sum_i \mu_i$. Then, for any $\alpha > 0$, $S = \sum_i X_i$ satisfies:

Example of concentration inequality.