Y is a random variable whose density is either:
f(y|H_0) = 2/3(y+1) for 0 <= y <= 1, and 0 otherwise
f(y|H_1) = 1 for 0 <= y <= 1, and 0 otherwise
How do I find the Bayes rule and the resulting error probabilities Pr(D_0|H_1) and Pr(D_1|H_0) for testing H_0 versus H_1 with equal priors and uniform costs (C_ii = 0 and C_ij = 1).