Past exam of the mathematics course of the University of Oxford / 2017 / Prelims / Mathematics III / 4 / b / i / Solution

Since $Y\ge 1$, its finite mean satisfies $1\le \mu <\infty$. Every $q_k=k{p}_k/\mu$ is nonnegative, andThus $(q_k)$ is a probability mass function. It defines the size-biased distribution of $Y$: an outcome of size $k$ receives $k$ times its original relative weight.