3. In a classification problem, suppose we would like to use discriminant analysis to classify the response Y into 3 classes (Y = 1,2,3) based on one predictor X. In the class k (k = 1,2,3), X follows a normal distribution N(uk, 0). Assume that the prior probability k = Pr(Y = k) is equal for all k. (a) Suppose = 2 = 03, find out the Bayesian decision boundary by dis- criminant analysis and corresponding decision rules. (b) If 01 02 03, derive the discriminant function and show that it is quadratic.