 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ia/paper-2/3f/c/solution

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

For any

t > 0

P (X \geq v) \leq e^{- t v} M_{X} (t) = e^{- t v + t^{2} /2} .

The minimum occurs at

t = v

\int_{v}^{\infty} \frac{e ^{- x^{2} /2}}{2 π} d x \leq e^{- v^{2} /2} .

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