Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 1 / 29K / c

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- Solution c

Solution

The one-observation score function is

S_{σ} (X) = - \frac{1}{σ} + \frac{X ^{2}}{σ ^{3}} .

Its variance, or equivalently minus the expected second derivative of the log-likelihood, is the Fisher information

I (σ) = \frac{2}{σ ^{2}} .

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