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$X$ and $Y$ are two independent variables, with variances $\sigma^2_x$ and $\sigma^2_y$ respectively.

Two other variables $W$ and $V$ are defined by $W=X+Y$ and $V=X-Y$.

Find $Cov(X,V)$ and $Cov(W,V)$

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closed as off-topic by Em., GoodDeeds, Silvia Ghinassi, user228113, Michael Albanese Mar 7 '16 at 5:54

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  • $\begingroup$ Hint: $\operatorname{Cov}(\bullet,\bullet)$ is bilinear. $\endgroup$ – user228113 Mar 7 '16 at 4:37
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Hint: Recall that covariance satisfies bilinearity,

$$\text{Cov}(aX+Y, Z) = a\text{Cov}(X,Z)+\text{Cov}(Y,Z)$$ and $$\text{Cov}(X,X) = \text{Var}(X).$$

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  • $\begingroup$ So Cov(X,V)=Cov(X,X-Y)=Cov(2X)+Cov(X-Y)? $\endgroup$ – ItsImpulse Mar 7 '16 at 3:32
  • $\begingroup$ No, try again.. $\endgroup$ – Em. Mar 7 '16 at 3:33
  • $\begingroup$ Sorry should the last term be -Cov(X,Y)? $\endgroup$ – ItsImpulse Mar 7 '16 at 3:38
  • $\begingroup$ No, try again.. $\endgroup$ – Em. Mar 7 '16 at 3:39
  • $\begingroup$ Cov(X,X) - Cov(X,Y)? $\endgroup$ – ItsImpulse Mar 7 '16 at 3:41

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