 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2008/o/5/i/solution

Independence makes a difference of the two normal sample means normal, with means subtracting and variances adding. Therefore

\overline{X} - \overline{Y} \sim N (μ_{X} - μ_{Y}, σ^{2} (\frac{1}{m} + \frac{1}{n})) .

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