Chebyshev's Inequality

Theorem
Let $X$ be a random variable.

Let $\expect X = \mu$ for some $\mu \in \R$.

Let $\var X = \sigma^2$ for some $\sigma^2 \in \R_{> 0}$.

Then, for all $k > 0$:


 * $\map \Pr {\size {X - \mu} \ge k \sigma} \le \dfrac 1 {k^2}$