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\begin{align*}\begin{aligned}\sigma^{2} &=\Sigma(x-\mu)^{2} P(x) \\&=(-1-0.4)^{2} \cdot 0.2+(0-0.4)^{2} \cdot 0.5+(1-0.4)^{2} \cdot 0.2+(4-0.4)^{2} \cdot 0.1 \\&=1.84\end{aligned}\end{align*}