Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 1 / 6H / d / Solution

The joint density depends on the sample throughnot merely through ${\sum }_i|X_i|$. For example, after padding with zeros when $n>2$, takeBoth samples have sum of absolute values $2$, butwhich depends on $\sigma$. The likelihood-ratio necessary condition for sufficiency fails, so

Solved by gpt-5.6-sol high.