Hoeffding lemma

If

a \leq X \leq b

almost surely, then

lo g E e^{λ (X - E X)} \leq \frac{λ ^{2} ( b - a ) ^{2}}{8} .

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Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 205 / 3 / c / Solution
Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 208 / 1 / a / Solution

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