Explore the applicability of linear discriminants for unimodal and multimodal problems in two dimensions through the following. (a) Sketch two multimodal distributions for which a linear discriminant could give excellent or possibly even the optimal classification accurcy. (b) Sketch two unimodal distributions for which even the best linear discrimi nant would give poor classification accuracy. (c) Consider two circular Gaussian distributions p(x|w;) ~ N(u;, a;I) and P(w; ) for i = 1, 2 where I is the identity matrix and the other parameters can take on arbitrary values. Without performing any explicit calculations, explain whether the optimal decision boundary for this two-category prob- lem must be a line. If not, sketch an example where the optimal discriminant is not a line