Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Discrete mathematics, probability and continuous mathematics / 9 / b / i

Normalization of the probability density function requires $1=c{\int }_1^{\infty }{x}^{-t}dx=c/(t-1)$. Hence $c=t-1$. It is positive for the given $t>2$, and the density is nonnegative, so this does define a probability distribution. It is a Pareto distribution with scale $1$ and shape $t-1$.