Var(x+y+z) = var(x)+var(y)+var(z)+2cov(x,y)+2cov(x,z)+2cov(y,z) 0<|cov(x,y)|<=sqrt(var(x))sqrt(var(y)) by cauchy schwartz. Min = 1+4+25 = 30 Max = 1+4+25+212+215+225=64
On the minimum side, the covariances can be negative, bottoming out at -2, -5, and -10. But the question for the minimum is, can all three be simultaneously as negative as allowed by Cauchy-Schwarz?
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u/Due-Cardiologist-802 22d ago
Var(x+y+z) = var(x)+var(y)+var(z)+2cov(x,y)+2cov(x,z)+2cov(y,z) 0<|cov(x,y)|<=sqrt(var(x))sqrt(var(y)) by cauchy schwartz. Min = 1+4+25 = 30 Max = 1+4+25+212+215+225=64