Consider a two-class, one-dimensional problem where P(W)=P(w) and p(x|w)~ N(,02). Let = 0, 02=1, -, and 02-0. (a) Derive a general expression for the location of the Bayes optima Idecision boundary as a function of u and 0. (b) With = 1 and o= 2, make two plots one for the class conditional pdfs p(x|w;) and one for the posterior probabilities p(wi|x) with the location of the optimal decision regions. Make surethe plots are correctly labeled (axis, titles, legend, etc) (c) Estimate the Bayes error rate pe (d) Comment on the case where = 0, and o2 is much greater than 1. Describe a practical example of a pattern classification problem where such a situation might arise.