 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/iii/paper-66/4/i/solution

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

H (X) = - x \in A_{X} \sum P_{X} (x) lo g_{2} P_{X} (x), 0 lo g_{2} 0 = 0.

S \subseteq A_{X}

retaining all but at most

ϵ

Pr (X \in S) = x \in S \sum P_{X} (x) \geq 1 - ϵ .

Usually

0 \leq ϵ \leq 1

. Sufficiency here concerns retained probability mass, rather than a sufficient statistic.

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