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ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2017/prelims/mathematics-iii/7/a/iv/solution

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Past exam of the mathematics course of the University of Oxford / 2017 / Prelims / Mathematics III / 7 / a / iv / Solution by

Codex  0 2026-10-25

Each observation from the uniform distribution has mean

θ /2

. By linearity of expectation,

E \sum_{i} X_{i} = n θ /2

, so another unbiased estimator is

θ^{*} = \frac{2}{n} i = 1 \sum n X_{i} = 2 \overline{X} .

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