Theorem 10.2.1. Chebyshev’s Theorem.
Given a random variable X with given mean \(\mu\) and standard deviation \(\sigma\text{,}\) for \(a \in \mathbb{R}^+\) ,
\begin{equation*}
P( \big | X - \mu \big | \lt a ) \gt 1 - \frac{\sigma^2}{a^2}
\end{equation*}