Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 35 / 2 / e / 1

Start with the Beta distribution draw in the Beta-binomial exchangeable coupling. Write $s=\alpha +\beta$ andThese are the expected value and variance of $p_M$. The fixed $n$ in this coupling is a dependence parameter chosen by the investigator, not necessarily the observed number of cups. The four numbered stages together address the single printed correlation request.