Markov's Inequality - Corollary: Chebyshev's Inequality

Corollary: Chebyshev's Inequality

Chebyshev's inequality uses the variance to bound the probability that a random variable deviates far from the mean. Specifically:

for any a>0. Here Var(X) is the variance of X, defined as:

Chebyshev's inequality follows from Markov's inequality by considering the random variable

for which Markov's inequality reads