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# hw4 - EE5620 Stochastic Processes 1 EE5620 Homework#4 Due...

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EE5620 Stochastic Processes 1 EE5620 - Homework #4 Due on Friday, 11/24/2006, in class Reading assignments: Section 4.1 Section 4.3, Gallager’s note. Problem assignments: 1. (20 points) Suppose you want to estimate a random vector x from observations y . You know the information about the first and second order statistics of the joint distribution of [ x T , y T ] T , but you don’t know the actual distribution itself. You want to design a robust estimator, one which has decent performance no matter what the joint distribution is. More precisely, for any estimator φ , let its worst-case performance e ( φ ) be defined as: e ( φ ) , max f x , y E £ || x - φ ( y ) || 2 / , where the maximum is taken over all joint distribution f with the given first and second order statistics. Find the estimator which has the optimal worst-case performance. Justify your answer carefully. 2. (10+10+10=30 points) Consider a communication link with received signal given by Y = X + S + Z, where X is the transmitted signal with mean μ and variance σ 2 X , S is a known

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hw4 - EE5620 Stochastic Processes 1 EE5620 Homework#4 Due...

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