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)*] .

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.