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Original solutions to past examinations of the probability, measure and martingales course of the University of Oxford.

Solutions to every part of all three questions of the probability, measure and martingales course of the University of Oxford Part B examination, sat on 5 June 2023. Source: original released PDF, bundle pages 288–291; paper pages 1–4. The native PDF confirms the endpoint defect in Question 2: its slope formula evaluates $f$ outside $[0,1]$ when $X=1$. We specify values on that null set below. Question 1(b)'s literal measurability assertion uses everywhere sign-valued random variables; for arbitrary versions with the stated probability distributions, it holds up to null sets, as explained in the solution.