 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-224/4/b/solution

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

For the distribution

Q_{C}

from part (a),

L (x) = - lo g_{2} Q_{C} (x) - lo g_{2} K .

Therefore

E_{P} L (X) = H (P) + D (P ∥ Q_{C}) - lo g_{2} K \geq H (P),

K \leq 1

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