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#1




Variance of weighted normal variables
I know this seems like a P question, but it appeared as a practice problem for MFE. Thus, I thought I'd ask here.
If I have two jointly normally distributed RVs, X and Y, with correlation rho, what is the variance of Z, with Z being aX  bY? I always thought the formula for Var[aXbY] = a^2Var[X]+b^2Var[Y]  2abCov[X,Y], but the solution had a plus instead of a minus in front of 2abCov[X,Y]. Does anyone know why this is? 
#3




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#4




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Isn't it because b = (1), so with your equation: Var[aXbY] = Var[aX+(b)Y] = (a^2)Var[X]+(b^2)Var[Y]  2a(b)Cov[X,Y] = a^2Var[X]+b^2Var[Y] + 2abCov[X,Y]
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#5




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The original equation without a different b does not have a minus in front of the Covariance term. There is an error with the practice problem OP had. 
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covariance, variance 
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