Covariance Question

Question

$X$ 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 $Cov(W,V)$

Hint: $\operatorname{Cov}(\bullet,\bullet)$ is bilinear. – Mar 07 '16 at 04:37 — , Mar 07 '16 at 04:37

score 1 · Accepted Answer · answered Mar 07 '16 at 03:29

1

Hint: Recall that covariance satisfies bilinearity,

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

answered Mar 07 '16 at 03:29

Em.

So Cov(X,V)=Cov(X,X-Y)=Cov(2X)+Cov(X-Y)? – ItsImpulse Mar 07 '16 at 03:32
No, try again.. – Em. Mar 07 '16 at 03:33
Sorry should the last term be -Cov(X,Y)? – ItsImpulse Mar 07 '16 at 03:38
No, try again.. – Em. Mar 07 '16 at 03:39
Cov(X,X) - Cov(X,Y)? – ItsImpulse Mar 07 '16 at 03:41
Yes.${}{}{}{}{}{}$ – Em. Mar 07 '16 at 03:42
I see now. Thank you very much – ItsImpulse Mar 07 '16 at 03:43
@ItsImpulse No problem. Considering giving up votes and check marks to respondents in all your posts. Good luck. – Em. Mar 07 '16 at 03:46

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