Conditional variance
Summary
Definition
- \(X,Y\) are two random variables. Let
\[Z={\left( Y-E\left( X \right) \right)}^2\]
- We define the conditional variance of \(Y\) given \(X\) as
\[Var\left( X \right)=E\left( X \right)=E\left( X \right)=E\left( X \right)-{\left( E\left( X \right) \right)}^2\]
Law of total variance
\[Var\left( Y \right)=E\left( Var\left( X \right) \right)+Var\left( E\left( X \right) \right)\]