Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 208 / 2 / b / Solution

The bounded differences property with constants $c_i$ meanswhenever $x$ and $x^{\prime }$ differ only in coordinate $i$. Conditional on $X_{-i}$, the range of $Z$ is therefore at most $c_i$. The range bound on variance givesSubstitution into the Efron–Stein inequality yields