 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2023/discrete-mathematics-probability-and-continuous-mathematics/9/b/ii/solution

The expected value is finite because

t > 2

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

The condition on

t

is precisely the first moment threshold for this parameterization of the Pareto distribution.

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