Variance
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What is the maximum variance of an indicator variable?
\(p(1-p)\) maximized for \(p=0.5\). -
Given independent random variables \(X\) and \(Y\), what is \(Var(aX + bY + c)\)?
- \(Var(X+a)=Var(X)\) for any constant \(a\).
- \(Var(aX)=a^2Var(X)\) for any constant \(a\).
- \(Var(X+Y)=Var(X)+Var(Y)\) for independent random variables \(X\) and \(Y\).
Applying those three rules we get that \(Var(aX + bY + c)=a^2\cdot Var(X) + b^2\cdot Var(Y)\)