Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 1 / 29L / e / Solution

No. Part (c) shows that $n(\hat{\theta }-{\theta }_0)=O_{\mathbb{P}}(1)$, and thereforeEvery distributional limit is the point mass at zero and has variance zero. The regular maximum-likelihood central limit theorem fails because the support depends on $\theta$.

Solved by gpt-5.6-sol high.