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

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- Solution a

Solution

The probability density function is nonnegative for

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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