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On the problem of classifying mechanical parts including four classes (bolt, nut, ring and scrap), Table 2 shows the loss incurred for assigning a part in class j to the class i, 1(w;|w; ) in terms of USD. true classes wi=bolt Wz=nut W3=ring W4=scrab w = bolt - 0.20 0.07 0.07 0.07 classes assigned w = nut 0.07 - 0.15 0.07 0.07 w = ring 0.07 0.07 - 0.05 0.07 W = scrap 0.03 0.03 0.03 0.03 Assume that for a given mechanical part (represented with feature vector x), the posterior probabilities are P(bolt x) = 0.21, P(nut x) = 0.30, P(ring x) = 0.29 and P(scrap x) = 0.20. Find the conditional and overall risk and find the assigned class