Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 223 / 3 / a

Randomly partition the observations into $k$ groups of size $m=n/k$, form the group means ${\overline{X}}_1,\dots ,{\overline{X}}_k$, and define the median-of-means estimator byChebyshev givesA binomial tail bound shows that at least half the groups are good with probability at least $1-e^{-k/8}\ge 1-\delta$. Thereforewith probability at least $1-\delta$.

Solved by gpt-5.6-sol high.