Theorem 26.1.2 (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-Noncommerci...