 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-2/11/a/solution

α > 0

. Its integral over the support is

\int_{1}^{\infty} α x^{- α - 1} d x = [- x^{- α}]_{1}^{\infty} = 1,

so it is normalized for every $α > 0$ . This is the unit-threshold Pareto distribution.

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