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4. [25points] This question is about the principal component analysis. Let random vector pr1 have the covariance matrix prp. Suppose the principal components are Y1, Y2, . . . , 13,. o [10points] Are the principal components necessarily unique? Justify your answer. 0 [15points] Suppose, in a given problem, after computing the eigenvalues of prp we obtain that the biggest eigenvalue A1 = 0.5(p + 1) and A2 = A3 = .. . = AP = 0.5. What is the proportion of total population variance due to the rst principal component? What is the value of this proportion in very large dimensions