Hoeffding's Inequality Explained: Exponential Confidence for Bounded Averages

We unpack Hoeffding's inequality, the 1963 result that bounds how far the average of independent bounded trials can drift from its expected value. We compare it with Chebyshev and the central limit theorem, explain why the bound decays exponentially with more data, and show how to use it to plan sample sizes. From coin flips to reliable AI systems, this episode reveals the math that underpins practical certainty in data.

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