Variance Properties: Understanding Var(aX+bY+c) & Solving for Var(aX+bY)

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SUMMARY

The discussion confirms that the variance of the linear combination Var(aX + bY + c) is equivalent to Var(aX + bY), as the addition of a constant does not affect variance. The property used to derive this conclusion is Var(aX + bY) = a²Var(X) + b²Var(Y) + 2abCov(X, Y). This property is essential for understanding how variance behaves under linear transformations.

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[SOLVED] Properties of variance

Would the Var(aX + bY + c) just be the Var(aX+bY) since adding a single number to the function doesn't change the variance. I would then be able to use the property:

Var(aX+bY)= a^2Var(X)+b^2Var(Y)+2abCov(X,Y)

Just wondering if anyone can confirm my reasoning here. Thanks.
 
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Correct.
 
Thank you, that's all I need. Mods can close.
 

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