Backing out a correlation

MediumRandom Variables Statistics~4m

For two variables with $\operatorname{Var}(X)=4$ and $\operatorname{Var}(Y)=9$ , you observe that the difference $X-Y$ has variance $7$ . What is the correlation $\rho$ between $X$ and $Y$ ? (to 2 decimals)

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Invert Var(X-Y) = Var X + Var Y - 2 Cov to solve for Cov, giving (4+9-7)/2.
Then rho = Cov / (sigma_X sigma_Y) = Cov / 6.

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0.5 (± 0.01)

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Backing out a correlation

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