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

For $q>1$, decreasing the second parameter by one gives another valid beta distribution density andNormalization therefore givesThe restriction $q>1$ is essential for this finite expected value; when $q=1$, the singularity near $1$ instead makes the expectation infinite.