Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 46 / 2 / b / ii / Solution

Evaluating the fitted linear discriminant analysis score givesThe fifth individual lies exactly on the discriminant boundary. Its two fitted posterior probabilities are equal, so the equal-prior Bayes classifier cannot prefer either species. A specified tie convention could assign it to one species, but such an assignment would not be evidence favoring that species.

In the sketch the solid line is the equal-prior boundary. The dashed line is the prior-dependent Gaussian discriminant boundary for the altered priors in (iii).