Bienaymé-Chebyshev Inequality

Theorem
Let $X$ be a random variable.

Let $\mathbb E \left[{X}\right] = \mu$ for some $\mu \in \R$.

Let $\operatorname{var} \left({X}\right) = \sigma^2$ for some $\sigma^2 \in \R_{> 0}$.

Then, for all $k > 0$:


 * $\mathbb P \left({\left\vert X - \mu \right\vert \ge k \sigma}\right) \le \dfrac 1 {k^2}$