\begin{proof} $$\mathbb{P}(|X-\mu|\ge\alpha)=\mathbb{P}(|X-\mu|^{2}\ge\alpha^{2})\le \frac{\mathbb{E}[|X-\mu|^{2}]}{\alpha^{2}}$$ with the inequality being an application of Markov’s Inequality. \end{proof}