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Bounded differences property

{c}
{wiki=McDiarmid's_inequality}

If $X_1,\ldots,X_n$ are <independent random variables> and $f$ has <bounded differences property>[bounded differences] constants $c_i$, then
$$
\mathbb P\bigl(f(X)-\mathbb Ef(X)\geq t\bigr)
\leq\exp\left(-\frac{2t^2}{\sum_i c_i^2}\right),
$$
and the same bound holds for the lower tail.

McDiarmid inequality

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 208 / 4 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 208 / 4 / c / Solution

McDiarmid inequality

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McDiarmid inequality

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