Fy(y)=P(Y<=y)=P(-lnX<=y)=P(ln(1/X)<=y)=P(1/X<=e^y)=P(X>=e^(-y))=1-F(e^(-y))
=1-e^(-y) (y>0)
fy(y)=F'y(y)=e^(-y)
E(X)=(0+1)/2=0.5
E(Y)=1/1=1
E(XY)= E(Ye^(-Y))=∫(0~无穷)ye^(-y)e^(-y) dy=0.5∫(0~无穷)(2y)e^(-2y) d(2y)/2=0.25gamma(2)=0.25(2-1)!=0.25
Cov(X,Y)=E(XY)-E(X)E(Y)=0.25-0.5=-0.25
D(X)=1/12
D(Y)=1/1^2=1
pxy=Cov(X,Y)/根(D(X)D(Y))=-(1/4)/(根(1/12))=-(根12)/4=-(根3)/2
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