(20 marks) Carry out LDA to classify the data points provided above to Class 1 and 2. Note that all calculations in Part (a) should be done by hand. The three steps involved are reproduced below for easy reference: Step 1. Apply LDA to project high-dimensional input vectors into one dimension. Step 2. Estimate , on the y-space for each of the two classes. Step 3. Place threshold on y for classification based on decision theory. Assume p1=0.5 . (Hint: Make use of the results obtained in the tutorial). In particular, show the steps in your computation of the following items: i. S1, S2, S, SB, w, Y1, Y2 in Step 1. ii. 1, 1, 2, 2 in Step 2. iii. The classification threshold obtained in Step 3. (Hint: Make use of the results obtained in the tutorial). (b) (20 marks) Write a Python function called LDA to verify your calculation in Part (a). The function should have a header: def LDA(X1, X2) where X1 and X2 are arranged in columns. In the function, codes should be written to (1) compute Item i, ii and iii in Part (a), (2) plot of all the data points with the projection vector superimposed and (3) f(y|Ck) for k = 1,2 and (4) f(Ck|y) for k = 1,2.

X1train=[23324432545328460065]X2train=[716915101311119171313914111511141012]Xtest=[40102.51012.5]