Mathematics, 14.07.2019 17:30 isaiahb30
Gwith the definition of covariance, prove cov[(ay − − d)] = accov(x, y ), where x, y are random variables and a, b, c, d are constants.
Answers: 1
![\mathrm{Cov}(X,Y)=\mathbb E[(X-\mathbb E[X])(Y-\mathbb E[Y])]](/tpl/images/0089/4107/ad827.png)
![\mathrm{Cov}(X,Y)=\mathbb E[XY-\mathbb E[X]Y-X\mathbb E[Y]+\mathbb E[X]\mathbb E[Y]]=\mathbb E[XY]-\mathbb E[X]\mathbb E[Y]](/tpl/images/0089/4107/51e0e.png)
![\mathbb E[(aX-b)(cY-d)]=\mathbb E[acXY-adX-bcY+bd]](/tpl/images/0089/4107/a0ec9.png)
![=ac\mathbb E[XY]-ad\mathbb E[X]-bc\mathbb E[Y]+bd](/tpl/images/0089/4107/f5193.png)
![\mathbb E[aX-b]=a\mathbb E[X]-b](/tpl/images/0089/4107/9565e.png)
![\mathbb E[cY-d]=c\mathbb E[Y]-d](/tpl/images/0089/4107/d0611.png)
![\mathbb E[aX-b]\mathbb E[cY-d]=ac\mathbb E[X]\mathbb E[Y]-ad\mathbb E[X]-bc\mathbb E[Y]+bd](/tpl/images/0089/4107/52d6b.png)
![\mathrm{Cov}(aX-b,cY-d)=ac(\mathbb E[XY]-\mathbb E[X]\mathbb E[Y])=ac\mathrm{Cov}(X,Y)](/tpl/images/0089/4107/58606.png)
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Gwith the definition of covariance, prove cov[(ay − − d)] = accov(x, y ), where x, y are random var...
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