Solution

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

{c}

A centered <random variable> $X$ is sub-Poisson in the right tail with variance parameter $\sigma^2$ when
$$
\log\mathbb E e^{\lambda X}\leq\sigma^2(e^\lambda-\lambda-1)
$$
for every $\lambda\geq0$.

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