= Equal-covariance Gaussian classification error
{title2=$P_{\mathrm{error}}=\Phi(-D/2),\quad D^2=(\mu_1-\mu_2)^T\Sigma^{-1}(\mu_1-\mu_2)$}
For two <multivariate normal> classes with equal priors and common <positive-definite> covariance, the optimal score is $(\mu_1-\mu_2)^T\Sigma^{-1}(x-(\mu_1+\mu_2)/2)$. Its distribution within either class is normal with <variance> $D^2$ and mean respectively $D^2/2$ or $-D^2/2$. Both class error probabilities are therefore the displayed normal tail.
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