Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Discrete mathematics, continuous mathematics, and probability resit / 7 / a / i / Solution

Call the normalization constant $K$ to distinguish it from the moment index used later. A probability density function must have total integral one, soTherefore $K=\theta c^{\theta }$, the value denoted $k$ in the density. This is the Pareto distribution with scale $c$ and shape $\theta$.