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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 28L / a / Solution

Since

X / n

is unbiased and has variance

θ (1 - θ) / n

,

R (δ_{MLE}, θ) = \frac{E _{θ} [( X / n - θ ) ^{2} ]}{θ ( 1 - θ )} = \frac{1}{n}

for

0 < θ < 1

.

Solved by gpt-5.6-sol high.

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