2. Followings are the mean and covariance matrix of marks for five courses based on an exam which is taken by 80 students is one area. x' = (39.0, 50.6, 50.6, 46.7, 42.3) 84.2 105.1 93.6 [302.3 125.8 100.4 125.8 170.9 84.2 S=100.4 111.6 110.8 105.1 116.11 93.6 110.8 120.5 97.9 217.9 153.8 116.1 97.9 120.5 153.8 294.4- (a) Determine correlation matrix. (b) Investigate whether all courses has same correlation. (c) Determine eigen value and vector for the matrix. (d) Write down the equations for the two most important principal components and give each variance and their interpretations. (e) Investigate how many principal components have different eigen value. (f) Determine 90% confidence interval for the first principal component's variance.