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A random sample of 11 observations yielded a sample mean [0.5, -4.2] and a sample variance-covariance matrix S 1 6 . Assume that the population is multivariate normal. (a) Consider a confidence ellipse for the mean vector at level 90%. What are the coordinates of points A-D, representing the "southeast". the "northwest", the "northeast", and the "southwest" of the ellipse respectively, depicted below? Not to scale C B A D M1 A (southeast) B (northwest) C (northeast) (southwest) (b) Now, suppose that S above is actually the value of known population covariance matrix 2. What are the coordinates of points A-D now? A (southeast) B (northwest) C (northeast) D (southwest (c) Under the original premise (i.e., S a sample covariance matrix, and > is unknown), use the projection method to obtain simultaneous 90% confidence intervals for the population means. Lower Upper (d) Under the original premise (i.e., S a sample covariance matrix, and > is unknown), use the Bonferroni method to obtain simultaneous 90% confidence intervals for the population means. Lower Upper