# WhatsApp Image 2023-10-12 at 5.28.07 PM

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(c) Suppose two-thirds of the data belong to the positive class and the remaining one-third belong to the negative class. What is the expected error of a classifier that predicts every test record to be positive? Answer: 33.33% There are 66.66% "+" and 33.33% "-" classes. The classifier predicts every test record to be "+". The Confusion Matrix for above classification problem Actual "+" Actual "-* Predicted "+" TP = 66.66% FP =33.33% Predicted "-° FN=0 TN=0 The expected error = (FP + FN) / (TP + FP + FN + TN) = 33.33%/100% = 33.33% (d) Repeat the previous analysis assuming that the classifier predicts each test record to be positive class with probability 2/3 and negative class with probability 1/3. Answer: 44.44%. There are 66.66% "+" and 33.33% "-" classes. The classifier predicts "+" with probability 2/3. TP = 66.66%o0f "+" data * 2/3 = 44 .44% and Hence FN = 22.22% The classifier predicts "-" with probability 1/3 TN = 33.33% of "-" data * 1/3 = 11.11% and hence FP = 22.22% The Confusion Matrix for above classification problem Actual "+" Actual *-* Predicted "+" TP = 44 .44% FP =22.22% Predicted "-" FN = 22.22% TN = 33.33% The expected error=(FP + FN)/ (TP + FP + FN + TN) = 44.44%/100% = 44.44%