Ps5 - Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.432 Stochastic Processes Detection and

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Unformatted text preview: Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.432 Stochastic Processes, Detection and Estimation Problem Set 5 Spring 2004 Issued: Thursday, March 4, 2004 Due: Tuesday, March 16, 2004 Reading: This problem set: Sections 3.3.3- 3.3.6, 3.4 Next: Sections 4.0- 4.5 and Section 4.7 except 4.7.5 Exam #1 Reminder: Our first quiz will take place Thursday, March 11, 9am- 11am . The exam will cover material through Lecture 8 (March 2) as well as the associated Problem Sets 1 through 4. You are allowed to bring one 8 1 × 11 sheet of notes (both sides). 2 Problem 5.1 (a) Let x if y 1 /x p y ( y ; x ) = , otherwise for x > 0. Show that there exist no unbiased estimators ˆ x ( y ) for x . (Note that because only x > are possible values, an unbiased estimator need only be unbiased for x > rather than all x .) (b) Suppose instead that 1 if y x x p y ( y ; x ) = , otherwise for x > 0. Does a minimum-variance unbiased estimator for x based on y exist?exist?...
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This note was uploaded on 01/11/2012 for the course EE 6.432 taught by Professor Prof.gregorywornell during the Spring '04 term at MIT.

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Ps5 - Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.432 Stochastic Processes Detection and

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