problem set3

# problem set3 - ELEC 531 STATISTICAL SIGNAL PROCESSING...

• Homework Help
• PresidentHackerCaribou10582
• 2

This preview shows pages 1–2. Sign up to view the full content.

ELEC 531: STATISTICAL SIGNAL PROCESSING Department of Electrical and Computer Engineering Rice University Fall 2007 Problem Set 3 Due: September 20, 2007 Problem 3.1 We make L observations X 1 , . . . , X L of a parameter θ corrupted by additive noise ( X l = θ + N l ). The parameter θ is a Gaussian random variable [ θ ∼ N ( m θ , σ 2 θ )] and N l are statistically independent Gaussian random variables [ N l ∼ N (0 , σ 2 N )]. (a) Find b θ MMSE ( X ), the MMSE estimator of θ . (b) Assuming m θ = 0, compute the resulting mean-squared error. (c) Find the conditional mean-squared error of b θ MMSE ( X ), i.e. compute E X | θ £ ( θ - b θ MMSE ) 2 | θ / . How does this answer compare with the result in part (b)? Again assume that m θ = 0. (d) Find the maximum a posteriori ( MAP ) estimator of θ defined as the maximizer of the a posteriori density, b θ MAP = arg max θ p ( θ | X ) . Compare this estimator to the MMSE estimator found in part (a). Assume m θ has a non-zero value. Problem 3.2 Imperfect Geiger Counter. A radioactive source emits N radioactive parti-

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern