Question

一道概率论与数理统计的题,图中38题

Answer 1

(1) P(XY=0)=P(X=0或Y=0)=P(X=0)+P(Y=0)-P(X=0,Y=0)

P(X=0,Y=0)=1/2+1/3-7/12=1/4

由0=P(XY=2)=P(X=1,Y=2)+P(X=2,Y=1)得：P(X=2,Y=1)=0

故P(X=2Y)=P(X=0,Y=0)+P(X=2,Y=1)=1/4

(2)E(X)=2/3,E(Y)=1,E(XY)=2/3,E(X^2)=1,E(Y^2)=5/3

D(X)=E(^2)-E^2(X)=5/9,D(Y)=E(Y^2)-E^2(Y)=2/3

cov(X-Y,Y)=cov(X,Y)-cov(Y,Y)=E(XY)-E(X)*E(Y)-D(Y)=-2/3

(3)cov(X,Y)=E(XY)-E(X)*E(Y)=0

故 ρ=0