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Propagation of uncertainty
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===Effect of correlation on differences=== If ''A'' and ''B'' are uncorrelated, their difference ''A'' β ''B'' will have more variance than either of them. An increasing positive correlation (<math>\rho_{AB} \to 1</math>) will decrease the variance of the difference, converging to zero variance for perfectly correlated variables with the [[homoscedastic|same variance]]. On the other hand, a negative correlation (<math>\rho_{AB} \to -1</math>) will further increase the variance of the difference, compared to the uncorrelated case. For example, the self-subtraction ''f'' = ''A'' β ''A'' has zero variance <math>\sigma_f^2 = 0</math> only if the variate is perfectly [[autocorrelation|autocorrelated]] (<math>\rho_A = 1</math>). If ''A'' is uncorrelated, <math>\rho_A = 0,</math> then the output variance is twice the input variance, <math>\sigma_f^2 = 2\sigma^2_A.</math> And if ''A'' is perfectly anticorrelated, <math>\rho_A = -1,</math> then the input variance is quadrupled in the output, <math>\sigma_f^2 = 4 \sigma^2_A</math> (notice <math>1 - \rho_A = 2</math> for ''f'' = ''aA'' β ''aA'' in the table above).
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