Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 4 / 17H / a / Solution

The unrestricted maximum-likelihood estimates are $(\bar{X},\bar{Y})$, while the null fixes both means at zero. HenceUnder the null this is ${\chi }_2^2$, so the size-$\alpha$ generalized likelihood-ratio test rejects exactly when