Chapter 27 Tail Inequalities
نویسنده
چکیده
Theorem 27.1.2 (Chebychev inequality) Let X be a random variable with μx = E[X] and σx be the standard deviation of X. That is σX = E [ (X − μx) ] . Then, Pr [|X − μX | ≥ tσX] ≤ 1 t2 . Proof: Note that Pr [|X − μX | ≥ tσX] = Pr[(X − μX) ≥ t2σ2X] . Set Y = (X − μX). Clearly, E [ Y ] = σX. Now, apply Markov inequality to Y . This work is licensed under the Creative Commons Attribution-Noncommercial 3.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/3.0/ or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA.
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