 Solution

ID: past-exam-of-the-options-i-for-mathematics-and-philosophy-course-of-the-university-of-oxford/2013/n/1/d/i/solution

E [\frac{1}{n} j = 1 \sum n X_{j}] = μ, Var (\frac{1}{n} j = 1 \sum n X_{j}) = \frac{1}{n ^{2}} j = 1 \sum n σ^{2} = \frac{σ ^{2}}{n} .

The expectation formula does not require independence; independence is used for the variance sum.

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