Limit Theorems and Related Topics
Francisco J. Samaniego · 2014
Theorem 5.1.1. (Chebyshev’s inequality) For any random variable X with finite mean µ and variance σ2, and for any ε> 0, P(|X−µ| ≥ ε)≤ σ 2 ε2 . (5.1) Proof. We give a proof in the continuous case. The proof of the discrete case is similar.