please answer part C in detail

B14 2018 4. Consider a two-class classification problem where the two classes, A and B, have the following class-conditional likelihoods: 1 p(x |A) = exp 2 1 p(x|B) = exp V8 The observable variable (feature vector), x, is real. (a) Sketch p(x | A) and p(x | B) over x. [4 marks] (b) Assuming that p(B) = 0.3086, determine the MAP classification rule, and hence write out the conditions under which an instance with feature vector x should be assigned to class B [5 marks] (c) Determine the classification rule under a loss function that is zero for correctly classified instances, and for which the loss of assigning to A when the class is actually B is half the loss of assigning to B when the class is actually A. Interpret your results for parts (b) and (c) and comment on the connections between them. [7 marks] B14 2018 4. Consider a two-class classification problem where the two classes, A and B, have the following class-conditional likelihoods: 1 p(x |A) = exp 2 1 p(x|B) = exp V8 The observable variable (feature vector), x, is real. (a) Sketch p(x | A) and p(x | B) over x. [4 marks] (b) Assuming that p(B) = 0.3086, determine the MAP classification rule, and hence write out the conditions under which an instance with feature vector x should be assigned to class B [5 marks] (c) Determine the classification rule under a loss function that is zero for correctly classified instances, and for which the loss of assigning to A when the class is actually B is half the loss of assigning to B when the class is actually A. Interpret your results for parts (b) and (c) and comment on the connections between them. [7 marks]