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Question Number 192254 by Spillover last updated on 13/May/23
$${Establish}\:{the}\:{formular}\:\: \\ $$$$\sigma_{{x}−{y}} ^{\mathrm{2}} =\sigma_{{x}} ^{\mathrm{2}} +\sigma_{{y}} ^{\mathrm{2}} −\mathrm{2}{r}\sigma_{{x}} \sigma_{{y}} \:\: \\ $$$${where}\:{by}\:{r}\:{is}\:{the}\:{correlation} \\ $$$${coefficient}\:{between}\:{x}\:{and}\:{y} \\ $$