1.P(A)=1/4,P(B|A)=1/3,P(A|B)=1/2,可得P(AB)=1/12,P(B)=1/6
P(X=0,Y=0)=P(A非B非)=1-P(A+B)=1-[P(A)+P(B)-P(AB)]=2/3
P(X=1,Y=0)=P(AB非)=P(A)-P(AB)=1/6
P(X=0,Y=1)=P(BA非)=P(B)-P(AB)=1/12
P(X=1,Y=1)=P(AB)=1/12 联合分布就可得出.
2.E(X)=1/4,E(Y)= 1/6,E(XY)=1/12,COV(X,Y)=E(XY)-E(X)E(Y)=1/24
D(X)=E(X2)-[E(X)]2=3/16,D(Y)=E(Y2)-[E(Y)]2=5/36
ρ=COV(X,Y)=COV(X,Y)/[√D(X)√D(Y)]=1/√15