Suppose three tests are administered to a random sample of college students. Let X1, ..., XN be observation vectors in R3 that list the three scores of each student, and for j = 1, 2, 3, let xj denote a student's score on the j th exam. Suppose the covariance matrix of the data is 2 6. Let y be an “index" of student performance, with y = c,x1 + C2X2 + C3X3 and cỉ + c² + c = 1. Choose c1, C2, C3 %3D %3D so that the variance of y over the data set is as large as possible. [Hint: The eigenvalues of the sample covariance matrix are 1 = 3, 6, and 9.1

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