It is said that classifying an observation to the class for which (4.12) is largest is equivalent to classifying an observation to the class for which (4.13) is largest. Prove that this is the case. In other words, under the assumption that the observations in the kth class are drawn from a N(k, 2) distribution, the Bayes' classifier assigns an observation to the class for which the discriminant function is maximized. 4.12 =pk(x)=l=1kl21exp(221(xl)2)k21exp(221(xk)2)

4.13 =k(x)=x2k22k2+log(k)