Use a random-number-generating routine to calculate the

Question

Question: Use a random-number-generating routine to calculate the 1000-num-ber sequence uk, and compute

x_k+1 = 0.8x_k + 0.6u_k, k = 1-1000, x₀ = 0.

(a) Compute the auto- and cross-covariance functions of uk and xk. Comment on the results.

(b) Compute and compare the histograms of uk and xk.

(c) Calculate the discrete Fourier transforms, spectra, and cross specira of uk and xk.