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How to prove the inequality for the standard deviation of a linear combination of two random variables

First, transform $σ_{v}^2$ into the form of a standard quadratic function. \begin{aligned} &\sigma _{v}^{2}=s^{2}\sigma _{1}^{2}+\left( 1-s\right) ^{2}\sigma _{2}^{2}+2s\left( 1-s\right) c_{12}\\ &...
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