例已知X,Y的联合分布为 X 1 0 0<p<1 1 p 0 p+9=1 0 0 q 求Cov(X,Y),Pxw 解 X 10 1 0 P p②
求 Cov (X ,Y ), ρXY 1 0 p q X P 1 0 p q Y P 例 已知 X ,Y 的联合分布为 X Y 1 0 1 0 p 0 0 q 0 < p <1 p + q = 1 解 1 0 p q X Y P
EX=p,EY=P DX=pq,DY=pq E(XY)=P Cov(X,Y)=E(XY)-EXEY=pq =1 Cov(X,Y) PxY-DX DY
DX pq DY pq EX p EY p = = = = , , E(XY ) = p 1 ( , ) ( , ) ( ) = = = − = DX DY Cov X Y Cov X Y E XY EXEY pq ρ XY