RP-HW4 - Kyung Hee University Department of Electronics and...

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1 Kyung Hee University Department of Electronics and Radio Engineering C1002900 Random Processing Homework 4 Spring 2010 Professor Hyundong Shin Issued: May 12, 2010 Due: May 26, 2010 (No acceptance of overdue submission) Reading: Course textbook Chapter 8, Lecture Notes VIII–IX HW 4.1 (a) Let   , X 01 . Show that there exist no unbiased estimators  ˆ X for . (b) Suppose instead that   , X 0 . Does a minimum-variance unbiased (MVU) estimator for based on X exist? If yes, determine MVU ˆ X . If no, explain. HW 4.2 The data , , , , n nn XA r W n N  1 are observed. The random variables ,, , N WW W 1 are i.i.d.   , 2 0 . Find the Cramér-Rao bound for A . Does an efficient estimator exist? If yes, what is it and what is its variance? For what values of r is it consistent? HW 4.3 Suppose , Yx W n 12 where x is an unknown constant, and W 1 and W 2 are independent zero-mean Gaussian ran- dom variables with  var ,i f var f . W x W x 1 2 1 10 20 (a) Find the Cramér-Rao bound for unbiased estimators of x based on observation
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2 Y Y Y 1 2 .
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This note was uploaded on 06/10/2010 for the course ELECTRONIC C1002900 taught by Professor Hyungdongshin during the Spring '10 term at Kyung Hee.

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RP-HW4 - Kyung Hee University Department of Electronics and...

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