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13. In many pattern classification problems one has the option either to assign the pattern to one of c classes, or to reject it as being unrecognizable. If the cost for rejects is not too high, rejection may be a desirable action. Let 0 i = j i, j =1, . ...c "(ail w ; ) = i=ctl otherwise, where 1, is the loss incurred for choosing the (c + 1) th action, rejection, and As is the loss incurred for making any substitution error. Show that the minimum risk is obtained if we decide w; if P(wilx) 2 P(w; |x) for all j and if P(wi |x) 2 1 - A,/As, and reject otherwise. What happens if dy = 0? What happens if Section 2.2 2. Suppose two equally probable one-dimensional densities are of the form p(x|wi) ce-lx-ail/bi for i = 1, 2 and 0