4.1 (Refer to Lecture 10) (20 points), Minimum Distance Classifier (a) Hand Calculation: The following pattern classes have Gaussian probability density functions: :{(0,0),(2,0),(2,2),(0,2)"} and @ :{(4,4),(6,4),(6,6),(4,6):} Assume that P(@ ) = P(@;) = and obtain the equation of the Bayes decision boundary between these two classes. Sketch the decision boundary by Matlab using x between 0 and 6 with increment 0.1. (b) Programming: Implement Naive mean classifier. Explanations of the datasets: (1) data_training txt has four columns of attributes: [class truth label, x location, y location, pixel intensity], each row is a sample point. (2) similarly, data_testing.txt has three columns: [x location, y location, pixel intensity]. Now we want to predict the class for all points in data_testing. txt. Implementation steps: (1) read data_training.txt, (2) compute and store the mean vector for each class, (3) for each testing point in data_testing txt, classify it to the class that its Euclidean distance towards the class mean is minimized. Show your codes along with two outputs: (1) your mean vector for each class. (2) your classification results for all testing points. Helpers: fopen, fscanf, unique. 4.2 (Refer to Lecture 13) (20 points) Probability is different from fuzzy set. Let x = John, S be the set of smart people, and I be the set of tall people. Let the probability (or fuzzy membership) of mS(x) = 0.9 and mT(x) = 0.9. (a) What is the probability of John being tall and smart