Consider a two-class, one-dimensional problem where p(! 1) = p(! 2) and p(xj! i) n(i; 2 i ). let 1 = 0, 2 1 = 1, 2 = , and 2 2 = 2. (a) derive a general expression for the location of the bayes optimal decision boundary as a function of and 2. (b) with = 1 and 2 = 2, make two plots using matlab: one for the class conditional pdfs p(xj! i) and one for the posterior probabilities p(! ijx) with the location of the optimal decision regions. make sure the plots are correctly labeled (axis, titles, legend, etc) and that the fonts are legible when printed. (c) estimate the bayes error rate pe. (d) comment on the case where = 0, and 2 is much greater than 1. describe a practical example of a pattern classi cation problem where such a situation might arise.