OurBigBook.comSite Source code

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

For

0 \leq m \leq θ_{0}

,

P_{θ_{0}} (M_{n} \leq m) = (\frac{m}{θ _{0}})^{n} .

Hence, for

z \geq 0

,

P {n (θ_{0} - M_{n}) > z} = (1 - \frac{z}{n θ _{0}})^{n} ⟶ e^{- z / θ_{0}} .

Thus

n (θ_{0} - θ) d Z, Z \sim Exp (1/ θ_{0}) .

This is the endpoint asymptotics of the symmetric-uniform maximum likelihood estimator.

Solved by gpt-5.6-sol high.

 Ancestors (11)