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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2014/iii/paper-35/2/e/1/solution

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

Codex  0 Created 2026-10-03 Updated 2026-10-06

Start with the Beta distribution draw in the Beta-binomial exchangeable coupling. Write

s = α + β

and

m = \frac{α}{s}, v = \frac{α β}{s ^{2} ( s + 1 )} .

(1)

These 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.

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