Variance Let μ=E[X]\mu=\mathbb{E}[X]μ=E[X] where E[X]\mathbb{E}[X]E[X] is the expected value of probability distribution XXX. Var(X)=⟨(x−μ)2⟩=⟨X2⟩−2μ⟨X⟩+μ2=⟨X2⟩−⟨X⟩2\begin{gather*} Var(X)=\left\langle (x-\mu)^2 \right\rangle=\left\langle X^2 \right\rangle-2\mu\left\langle X \right\rangle+\mu^2\\ =\left\langle X^2 \right\rangle-\left\langle X \right\rangle^2 \end{gather*}Var(X)=⟨(x−μ)2⟩=⟨X2⟩−2μ⟨X⟩+μ2=⟨X2⟩−⟨X⟩2