A random vector ((xi, eta)) is normally distributed; (boldsymbol{M} xi=a, mathbf{M} eta=b, mathbf{D} xi=sigma_{1}^{2}), (D eta=sigma_{2}^{2}), and

Question:

A random vector $(\xi, \eta)$ is normally distributed; $\boldsymbol{M} \xi=a, \mathbf{M} \eta=b, \mathbf{D} \xi=\sigma_{1}^{2}$, $D \eta=\sigma_{2}^{2}$, and $R$ is the correlation coefficient of $\xi$ and $\eta$. Prove that $R=\cos q \pi$ where $q=\mathbf{P}\{(\xi-a)(\eta-b)<0\}$.

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