Solution
= Solution
The <bivariate normal distribution> has density
$$
\boxed{
f(x_1,x_2)
=\frac1{2\pi\sigma_1\sigma_2\sqrt{1-\rho^2}}
\exp\left\{
-\frac1{2(1-\rho^2)}
\left[
\frac{(x_1-\mu_1)^2}{\sigma_1^2}
-\frac{2\rho(x_1-\mu_1)(x_2-\mu_2)}
{\sigma_1\sigma_2}
+\frac{(x_2-\mu_2)^2}{\sigma_2^2}
\right]\right\}.}
$$