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# ps5 - n = 1 and n> 1 separately Problem 4(Poor Ch 4 Pr 11...

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EE 806, Detection and Estimation Theory May 12, 2008 OSU, Spring 2008 Due: May 19, 2008 Problem Set 5 Problem 1 Let Θ be a random variable with pdf w ( θ ) and let the conditional pdf of Θ given the observation ~ Y be w ( θ | ~ Y ). Show that the minimum mean absolute error (MMAE) estimate ˆ θ MMAE ( ~ y ) is the conditional median (as given in lecture notes) of w ( θ | ~ Y ). ( Hint: For a non-negative random variable X , E [ X ] = R 0 P ( X > x ) dx .) Problem 2 - (Poor, Ch. 4, Pr. 6) You don’t need to solve for ˆ θ MMAE in closed form. Problem 3 - (Poor, Ch. 4, Pr. 8) In part (c), consider the cases
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Unformatted text preview: n = 1 and n > 1 separately. Problem 4 - (Poor, Ch. 4, Pr. 11) Replace “What happens when. ..” with “What happens when (i) n → ∞ assuming | α | < 1, (ii) q 2 → ∞ , (iii) q 2 → 0”. In many problems of this sort it is extremely important to consider the support of the various pdfs. I suggest using the “indicator function” notation I A ( x ) = ( 1 x ∈ A x / ∈ A for set A . For example, a unit-exponential r.v. Y has pdf f Y ( y ) = e-y I [0 , ∞ ) ( y ). 1...
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