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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2023/discrete-mathematics-probability-and-continuous-mathematics/7/b/iii/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Discrete mathematics, probability and continuous mathematics / 7 / b / iii / Solution by

Codex  0 2026-10-25

Compute the conditional expectation from the possible increments:

E [R_{k + 1} ∣ R_{k} = r] = r + \frac{( n - r ) ^{2} - r ^{2}}{n ^{2}} = 1 + (1 - \frac{2}{n}) r .

(1)

Therefore $α = 1$ and $β = 1 - 2/ n$ . This calculation uses the conditional independence of the two selections, not independence of the successive counts

R_{k}

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