 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2014/discrete-mathematics-continuous-mathematics-and-probability/9/a/i/solution

A probability density function must be nonnegative and integrate to one. For

c > 0

\int_{1}^{\infty} c x^{- c - 1} d x = [- x^{- c}]_{1}^{\infty} = 1.

c = 0

the function is identically zero, while

c < 0

makes it negative on

x > 1

. Thus

c > 0

is necessary and sufficient. The resulting law is a Pareto distribution with scale one and shape

c

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