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Answers for “偏导数的几何解释与不确定性传播有什么关系?”

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Independent uncertainties are added in quadrature because they represent random effects that can push a measurement up or down. If the effects are random and independent, their combined influence is neither always cancelling nor always additive.

Conditions: The two uncertainty effects are random.; The two effects are independent from one another.; The combination is modeled by a perpendicular geometric construction.