1. Find the joint p.d.f. of the signal from Exercise 8.5.1 at t1 = 1, t2 = 1.5, and t3 = 2.5. Write the integral formula for P(0 ≤ X(1) ≤ 1, -1 ≤ X(1.5) ≤ 3, 0 ≤ X(2.5) ≤ 2).
Evaluate the above probability numerically.
2. Show that if a 2D Gaussian random vector Y- = (Y1, Y2) has uncorrelated components Y1, Y2, then those components are statistically independent random quantities.