answer all questions with explanation

7. Let X ~ N(0, R) where R is a p x p symmetric positive-definite matrix with an eigen decomposition of the form R = EAEt. a Calculate the covariance of X = EX, and show that the components of X are jointly independent Gaussian random variables. (Hint: Use the result of problem 5 above.) b) Show that if Y = EA1/2W where W ~ N(0, I), then Y ~ N(0, R). How can this result be of practical value