Normalization of the <probability density function> requires $1=c\int_1^{\infty}x^{-t}\,dx=c/(t-1)$. Hence \b[$c=t-1$]. 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 $t-1$.

Solution

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 / Solution

 Solution (source code)