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

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- Solution iv

Solution

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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