Introduction to Probability · Problem 8.1.14

Law of Large Numbers — Grinstead & Snell

Mathematics — Probability · chebyshev-inequality-analogue

Problem

Prove the following analogue of Chebyshev's Inequality: P(∣X−E(X)∣≥ϵ)≤1ϵE(∣X−E(X)∣).P(|X - E(X)| \geq \epsilon) \leq \frac{1}{\epsilon} E(|X - E(X)|).

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