Question: Consider two classes 0 and 1 with P (0) = 0.6. Suppose that the conditional probability density functions of the feature x are p(x|0) =

Consider two classes 0 and 1 with P (0) = 0.6. Suppose that the conditional probability density functions of the feature x are p(x|0) = 1 for 0 ≤ x ≤ 1 and p(x|1) = 2x for 0 ≤ x ≤ 1.

(a) What is the feature space?

(b) What are the possible decision rules?

(c) What is the optimal (Bayes) decision rule? Draw a picture indicating the intervals where the decision is one and where the decision is zero.

(d) What is the minimum (Bayes) error rate?

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