In: Statistics and Probability
Suppose that we have a single input variable X and all possible values of X is {0, 1, 2}. Also, suppose that we have two groups for outcomes (i.e., Y = 1, 2). It is known that the X|Y = 1 has Binomial(2, 0.7) and X|Y = 2 has the discrete uniform. In addition, P(Y = 1) = 0.3.
(1) Predict Y for X = 0, 1, 2, respectively, using the Bayes classifier.
(2) Compute the overall Bayes error rate.