 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2023/prelims/mathematics-iii/6/b/ii/solution

The condition

t > 2

guarantees a finite first moment. Direct integration gives

E [X] = (t - 1) \int_{1}^{\infty} x^{1 - t} d x = \frac{t - 1}{t - 2} .

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