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For two random variables $X$, $Y$, how can I calculate the $\text{Cov}(X,Y)$ given that $\text{Var}(X+Y)=1$ and $\text{Var}(X-Y)=2$?

I tried this but I'm missing something:

$\text{Var}(X+Y)=\text{Var}(x)+\text{Var}(Y)+2\text{ Cov}(X,Y)=1$

$\text{Var}(X-Y)=\text{Var}(X+(-Y))=\text{Var}(X)+\text{Var}(Y)-2\text{ Cov}(X,Y)=2$

But I don't know how to proceed.. Any ideas?

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  • $\begingroup$ subtract $V(X)+V(Y)-2Cov(X,Y)$ from $V(X)+V(Y)+2Cov(X,Y)$ and then rescale $\endgroup$ – Henry Sep 17 '17 at 18:45
  • $\begingroup$ Jesus that was simple! I can't believe I didn't see it lol. Thanks! $\endgroup$ – VakiPitsi Sep 17 '17 at 18:57

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