X is 10-dimensional gaussian 0i random vector since x is

Question

X is 10-dimensional Gaussian (0,I) random vector. Since X is zero mean, R_X = C_X = I. We will use the method of Problem 7.3.7 and estimate R_X using the sample correlation matrix

For n ∈ {10, 100, 1000, 10,000}, construct a Matlab simulation to estimate

Problem 7.3.7

An experiment produces a zero mean Gaussian random vector X = [X₁ ··· X_k] with correlation matrix R = E[XX']. To estimate R, we perform n independent trials, yielding the iid sample vectors X(1), X(2), . . . , X(n), and form the sample correlation matrix

(a) Show  (n) is unbiased by showing E[ (n)] = R.

(b) Show that the sequence of estimates  (n)is consistent by showing that every element  ij(n) of the matrix  converges to R_ij . That is, show that for any c > 0,