Suppose y is a random variable whose density is either:

f(y|H0) = {2/3(y+1), 0<=y<=1

{0, else

f(y|H1) = {1, 0 <= y <= 1

{0, else

Find the Bayes rule and the resulting error probabilities Pr(D0 | H1) and Pr(D1 | H0) for testing H0 versus H1 with equal priors and uniform costs (Cii = 0, Cij = 1)