6 a) Consider a document classification problem where documents are represented as vectors in a high-dimensional space, and the class labels are modeled using a multivariate normal distribution. In this scenario, we have two classes, Class A and Class B. Mean vector for documents in Class A: = [2, 3, 1]^ Covariance matrix for Class A: = 1 0.5 0.3 | 0.5 2 0.2 0.3 0.2 1 Mean vector for documents in Class B: = [0, 1, 4]^ Covariance matrix for Class B: = 1.5 0.1 0.4 0.1 1.8 0.6 0.4 0.6 2 Calculate the probabilities of the document represented by the vector = [1, 2, 0] belonging to Class A and Class B based on the multivariate normal distribution. Determine the predicted class for the document. b) Now suppose the covariance matrix for both class A and B is . Calculate the probabilities of the document represented by the vector = [1, 2, 0] belonging to Class A and Class B. Determine the predicted class for the document. What are the advantages and the assumptions made when using the shared covariance matrix compared to the scenario where separate covariance matrices are used for each class