求:D(X),D(Y),Cov(X,Y).
(1)E(X)=E(Y)=-3×0.2+3×0.2=0,E(X^2)=E(Y^2)=9×0.2+9×0.2=3.6
D(X)=E(X^2)-(E(X))^2=3.6,D(Y)=E(Y^2)-(E(Y))^2=3.6
(2)XY可能取值有:0、9、-9
P(XY=0)=0.84,
P(XY=9)=0.08,
P(XY=-9)=0.08,
所以E(XY)=0
COV(X,Y)=E(XY)-E(X)E(Y)=0
求:D(X),D(Y),Cov(X,Y).
(1)E(X)=E(Y)=-3×0.2+3×0.2=0,E(X^2)=E(Y^2)=9×0.2+9×0.2=3.6
D(X)=E(X^2)-(E(X))^2=3.6,D(Y)=E(Y^2)-(E(Y))^2=3.6
(2)XY可能取值有:0、9、-9
P(XY=0)=0.84,
P(XY=9)=0.08,
P(XY=-9)=0.08,
所以E(XY)=0
COV(X,Y)=E(XY)-E(X)E(Y)=0