Problem 5. Let X = [X1,..., Xn]' be a random vector where each component X; is a real-valued random variable (think of a real-valued random variable as giving you a random number in R). Let µ e R" be the expected value of X, µ = E [X], which means that Hi = E [X;] (you do not need to know what an expected value is to solve this problem, but you can think of it as giving the mean or average of a random variable). Recall that the covariance matrix of X is defined by Cov(X) = E [(X – µ)(X – µ)*] .

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