상관계수

공분산 (Covariance)

$Cov(X,Y)=E[(X-\mu_1)(Y-\mu_2)]=E(XY)-\mu_1\mu_2$

 

상관계수 (Correlation coefficient)

$\rho=\frac{E[(X-\mu_1)(Y-\mu_2)]}{\sigma_1\sigma_2}=\frac{Cov(X,Y)}{\sigma_1\sigma_2}$

 

조건부 기댓값

$E(Y|X)=\mu_2+\rho \frac{\sigma_2}{\sigma_1}(X-\mu_1)$

$E(Var(Y|X))=\sigma_2^2(1-\rho^2)$