Consider the following classification problem.. We first choose the label Y ∼ Bernoulli( 1 2 ), which is 1 with probability 1 2 . If Y = 1, then X ∼ Bernoulli(p); otherwise, X ∼ Bernoulli(q). Assume that p > q.
Required:
a. What is the Bayes optimal classifier, and what is its risk?
b. What is the Bayes optimal classifier?