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