Bivariate normal distribution
= Bivariate normal distribution
{wiki}
= Bivariate normal density
{synonym}
For means $\mu_i$, standard deviations $\sigma_i$, and correlation $\rho$, the standardized quadratic form in the density is
$$
\frac1{1-\rho^2}
\left[
\frac{(x_1-\mu_1)^2}{\sigma_1^2}
-\frac{2\rho(x_1-\mu_1)(x_2-\mu_2)}{\sigma_1\sigma_2}
+\frac{(x_2-\mu_2)^2}{\sigma_2^2}
\right].
$$