covarance
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Covariance
Covariance
\begin{eqnarray*} Cov[X, Y] & = & E[(X-EX)(Y-EY)] \\ & = & E[XY] - (EX)(EY) \\ \end{eqnarray*}
\begin{eqnarray} E[(X−EX)(Y−EY)] \nonumber \\ & = & E[XY−X(EY)−(EX)Y+(EX)(EY)] \\ & = & E[XY]−(EX)(EY)−(EX)(EY)+(EX)(EY) \\ & = & E[XY]−(EX)(EY)\\ \end{eqnarray}
위 $[1]$에서 $[2]$가 되는 이유는 $E[X], E[Y]$ 가 상수이기 때문. 가령,
\begin{eqnarray*}
E[X*2] & = & 2*E[X]
\end{eqnarray*}
위처럼 $ E[X] = \mu$ 로 보면
\begin{eqnarray*}
E[X*\mu] & = & \mu*E[X] \\
& = & E[X]E[X]
\end{eqnarray*}
covarance.1665591084.txt.gz · Last modified: 2022/10/13 01:11 by hkimscil