As shown in the decision tree, there are two available actions (a, and a,) and two states of nature (0, and 02). Additional information about the states of nature can be obtained by performing an experimental test (T) and its likelihood functions are given in the following table. , (p) 0 , (1-P) e, (p) -100 -50 az e, (1-p) -20 Likelihood function, P(20) 0 02 2 0.7 0.4 0.3 0.6 (a) Compute the posterior probability of each state of nature. (b) Compute the expected value of test T and the expected value of perfect test. You may have to draw plots (p vs. E[T] and p vs. E[PT]) in one figure