1. A zero-mean Gaussian random signal has the autocorrelation function of the form γX(τ) = 10e-0.1|τ| cos 2πτ.
Write the covariance matrix for the signal sampled at four time instants separated by 0.5 seconds.
2. Find the joint p.d.f. of the signal from Exercise 8.5.1 at t1 = 1 and t2 = 2.5. Write the integral formula for P(0 ≤ X(1) ≤ 1, 0 ≤ X(2.5) ≤ 2).
Evaluate the above probability numerically.