Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 210 / 1 / b / Solution

For $q\ge 2$, $q!\ge 23^{q-2}$. Hence, for $0\le \lambda <3$,Substitution into the defining moment-generating function bound shows that $X$ is sub-Gamma in the right tail with variance parameter ${\sigma }^2$ and scale parameter $1/3$.