# Markov's Inequality

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## Intuition

Markov's Inequality is an example of a **concentration inequality**, an inequality that provides bounds on how a random variable (in this case, X) differs from some value (in this case, a). Markov's inequality is useful because they apply to any non-negative random variable. Notice how the bound depends on E(X) and a. If X returns large values on average (E(X) is large) then it is likely X is large. Similarly if E(X) is small, then it likely that X is small. Bigger E(X) means higher probability, so E(X) intuitively goes in the numerator. a is our definition of large. It is more likely that I am taller than 3' than it is that I am taller than 10', Pr(X \geq 3) \geq P(r(X \geq 10). This suggests that increasing a decreases the probability, so a goes in the denominator.
ddd

## Examples

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