 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-3/26l/d/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

On disjoint events

A_{n}

with

P (A_{n}) = c / n^{2}

X_{n} = n 1_{A_{n}}

. Then

X_{n} \to 0

E X_{n}^{2} = c

, but any common dominator has integral at least

\sum_{n} n P (A_{n}) = c \sum 1/ n = \infty

. Thus no integrable dominating variable exists.

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