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# ps5 - Massachusetts Institute of Technology Department of...

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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 0 y 1 /x p y ( y ; x ) = , 0 otherwise for x > 0. Show that there exist no unbiased estimators ˆ x ( y ) for x . (Note that because only x > 0 are possible values, an unbiased estimator need only be unbiased for x > 0 rather than all x .) (b) Suppose instead that 1 if 0 y x x p y ( y ; x ) = , 0 otherwise for x > 0. Does a minimum-variance unbiased estimator for x based on y exist?

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