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The variance of \(X\) is:

\(\begin{aligned}\operatorname{Var}[X] & =\mathbf{E}\left[(X-\mathbf{E}[X])^2\right] \\& =\int_{\Omega}(X(\omega)-\mathbf{E}[X])^2 P(d \omega)=\int_{\mathbb{R}}(x-\mathbf{E}[X])^2 \mu(d x)\end{aligned}\)

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