Chapter 7

Complete the following 9 problems:

1. Exercise 7-16, p. 325
   • Hint: For this problem, use the identity \(\text{Cov}( \mathbf{a}^{T} \mathbf{X}, \mathbf{b}^{T} \mathbf{X}) = \mathbf{a}^{T} \text{Var}(\mathbf{X}) \mathbf{b} = \mathbf{a}^{T} \mathbf{V} \mathbf{b}\). This is a generalization of the result that \(\text{Var}(\mathbf{a}^{T} \mathbf{X}) = \text{Cov}( \mathbf{a}^{T} \mathbf{X}, \mathbf{a}^{T} \mathbf{X}) = \mathbf{a}^{T} \mathbf{V} \mathbf{a}\).
2. Exercise 7-24, p. 327
3. Exercise 7-50, p. 359
4. Exercise 7-56, p. 360
5. Exercise 7-61, p. 368
   • For this and the following problem, see the list of properties of Gaussian random vectors in the green box on page 363 of Asimow & Maxwell.
6. Exercise 7-64, p. 368
7. Exercise 7-65, p. 370
8. Exercise 7-66, p. 371
9. Sample Exam Problem 20, p. 376