Markov's Inequality

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Markov's Inequality states that given an $a$ that is positive, and an $X$ that is non-negative, the following holds:

P (X \geq a) \leq \frac{E (X)}{a}

It is possible to deal with random variables that are negative by taking the absolute value so that:

P (| X | \geq a) \leq \frac{E (| X |)}{a}

It can be derived fairly simply by taking the expected value of the two functions shown above.
It is a general case of Chebyshev's Inequality.

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