Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics III / 6 / b / i

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- Solution i

Solution

Normalization of the probability density function requires

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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