Past exam of the computer science course of the University of Oxford / 2015 / Probability and computing / 1 / c / Solution

Chebyshev's inequality assumes a real random variable $X$ with finite expectation $\mu$ and finite variance ${\sigma }^2$. For every real $a>0$,No independence assumption is needed. Applying Markov's inequality to the nonnegative random variable $(X-\mu {)}^2$ proves the formula, including the zero-variance case.