Question 2 (8 Marks) This question does not required any software. Suppose the random variables X1, X, have the covariance matrix with the eigenvalues and corresponding eigenvectors given as follows A1 =3.618, e1 = (-0.357, -0.934) 12= 1.382, en = (-0.934, -0.357). Denote the principal components by Y, and Y2. (a) (2 marks) Write down Y, and Yz explicitly. (6) (3 marks Compute the proportion of the total variance explained by each of the principal components. (c) (3 marks) Are Y, and Y, uncorrelated? Give your reasoning