This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.432 Stochastic Processes, Detection and Estimation Problem Set 4 Spring 2004 Issued: Thursday, February 26, 2004 Due: Thursday, March 4, 2004 Reading: This problem set: Sections 1.7, 3.2.5, 3.3.1, 3.3.2 Next: Sections 3.3.3 3.3.6, 3.4 Exam #1 Reminder: Our first quiz will take place Thursday, March 11, 9 am 11 am. The exam will cover material through Lecture 8 (March 6), as well as the associated Problem Sets 1 through 4. You are allowed to bring one 8 1 11 sheet of notes (both sides). Note that there 2 will be no lecture on March 11. Problem 4.1 Suppose w , z are scalar random variables, and that 1 / 2  z  < 1 p z ( z ) = . otherwise You are told that the Bayes leastsquares estimate of w given an observation z is 1 1 / 2 z w BLS = sgn z = , 2 1 / 2 otherwise and the associated meansquare estimation error is BLS = 1 / 12. However, you would prefer to use the following adhoc estimator w AH = z . w AH ) = E [ w (a) Is it possible to determine b ( w AH ], the bias of your new esti mator, from the information given? If your answer is no, briey explain your reasoning. If your answer is yes, calculate b ( w AH )....
View
Full
Document
 Spring '04
 Prof.GregoryWornell
 Electrical Engineering

Click to edit the document details