 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ia/paper-2/11f/c/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Similarly,

E [2^{2 X_{1}}] = \sum_{leaves v} 2^{d (v)} \leq ℓ 2^{b} .

Thus

Var (L) \leq ℓ 2^{b} / n

P (\frac{∣ L - ℓ ∣}{ℓ} \geq α \frac{2 ^{b}}{n ℓ}) \leq \frac{1}{α ^{2}} .

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