Let $\boldsymbol{X}\in\mathbb{R}^d$ be a random vector and $\boldsymbol{X}^{(1)},\boldsymbol{X}^{(2)},...,\boldsymbol{X}^{(n)}$ are $n$ independent observations. Also $f: \mathbb{R}^{d\times n} \rightarrow \mathbb{R}$ and $|f(\boldsymbol{X}^{(1)},\boldsymbol{X}^{(2)},...,\boldsymbol{X}^{(i)},...,\boldsymbol{X}^{(n)})-f(\boldsymbol{X}^{(1)},\boldsymbol{X}^{(2)},...,\boldsymbol{X'}^{(i)},...,\boldsymbol{X}^{(n)})|\leq c_i$. Is it true that :
$\text{Pr}[|f-\mathbb{E}f| \geq\epsilon] \leq 2 \exp(\frac{-2\epsilon ^2}{\sum _i c^2_i}) $ ? Notice that the elemements of $\boldsymbol{X}$ are not independent.