Past exam of the mathematics course of the University of Cambridge / 2026 / ib / Paper 1 / 17H / iv / Solution

The displayed linear form is centred normal with variance $n^{-1}{X}_{1j}^T(I-P_0)X_{1j}\le n^{-1}\Vert X_{1j}{\Vert }^2=1$. The normal tail bound proves the claim.

Solved by gpt-5.6-sol high.