1. The ACT Math, ACT Science, ACT Reading, and ACT Writing scores of 20 students are given as follows: Students Subjects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ACT Math 15 16 20 22 19 24 23 25 30 24 27 25 30 32 28 27 29 26 28 29 ACT Science 17 18 19 23 22 26 20 27 30 28 25 23 32 28 30 23 29 26 24 30 ACT Reading 20 18 21 22 22 28 22 23 25 30 29 29 32 33 32 33 29 30 26 31 ACT Writing 18 15 18 19 18 22 20 19 27 28 27 28 30 29 30 27 29 28 24 29 Considering x = (X X2 X3 X4)' to be the random vector consisting of four random components X, X2, X3, X4 that denote scores in ACT Math, ACT Science, ACT Reading, and ACT Writing exams for a student, answer the following questions: a) Obtain the sample mean x, sample covariance matrix Sx, and sample correlation matrix Rx of the random vector x. b) Obtain the generalized sample variance |S| and the total sample variance tr (S). c) Define u = x + x and v= x3 + x4. Denote y = (u). Obtain the sample mean y, sample covariance matrix Sy, and sample correlation matrix Ry of the random vector y. d) Find the generalized sample variance Syl and the total sample variance tr(Sy) and compare with your results in b). Comment on your findings.