(a) (20 marks) Use the Gaussian Discriminant Analysis method to come up with a mathematical description of the decision boundary used to classify Class 1 and 2. Use the training data to train the model and determine the decision boundary. Then classify each of the test points based on the posterior probabilities (1|) and (2|). In your submission, show the steps in your computation of the following items.

i. : The prior probability of Class 1; ii. : The mean vectors of the two classes; iii. : The covariance matrices of the two classes and the mean covariance matrix; iv. and 0 in the decision boundary equation: +0 =0.

(20 marks) Write a Python function called GaussianDiscriminantAnalysis. The function header should have the following form: def GaussianDiscriminantAnalysis(X1, X2) where data points in X1 and X2 are arranged in columns. In the function, codes should be written to (1) compute Item i, ii, iii and iv in Part (a) and the decision boundary and (2) plot of all the training data points with the decision boundary superimposed. You are encouraged to use the matlabplotlib.pyplot library for plotting.