Problem 1. The feature space consists of three possible points (events) A, B, C, which occur with probability 0.1, 0.4, 0.5, respectively. For each event there are two possible labels +1 or -1, which happen with probability 0.8, 0.3 and 0.1 respectively (that is, P(1|A) = 0.8, P(1|B) = 0.3, P(1 C) = 0.1). Determine the Bayes optimal classifier (as a function of the event, A,B,C). What is the expected loss of the Bayes optimal classifier