 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ia/paper-2/3f/b/ii/solution

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

t > 0

Pr (S \geq 2 n) \leq exp {- 2 n t + n (e^{t} - 1)} .

The exponent is minimized when

e^{t} = 2

, so take

t = lo g 2

. Then

Pr (S \geq 2 n) \leq exp {n (1 - 2 lo g 2)} = (\frac{e}{4})^{n} .

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