 Solution

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

1 = c \int_{1}^{\infty} x^{- t} d x = \frac{c}{t - 1} .

Hence

c = t - 1

. The distribution is a Pareto distribution with minimum one and shape parameter

t - 1

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