Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 208 / 4 / d / Solution

The coordinate-deletion functions from part c show that $Z$ is weakly self-bounding. Its negative centered moment-generating function therefore satisfies the lower-tail concentration for a weakly self-bounding function estimateApplying the Chernoff bound, for every $\lambda \ge 0$,The exponent is minimized at $\lambda =t/\mathbb{E}Z$, giving