Given training data where under 0-1 loss.

Let , Let denote the Bayes risk.

a) Show that

b) Show that equality holds above if X and Y are independent.

c) Exhibit a join distribution where X and Y are not independent but

Solution so far:

a) Suppose that is the Bayes learner, then:

I konw that mine must be wrong because it doesn't help me with the next two problems, please help thanks!