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1. An innovations sequence and its applications. Let [Y1 YE; Y3 X ]T be a zeromean random vector with covariance matrix 1 0.5 0.5 0 0.5 1 0.5 0.25

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1. An innovations sequence and its applications. Let [Y1 YE; Y3 X ]T be a zero—mean
random vector with covariance matrix 1 0.5 0.5 0
0.5 1 0.5 0.25
0.5 0.5 1 0.25 0 0.25 0.25 1 a. Let Y = [F 17}; YET be the innovations sequence of ‘1”? 2 [Y1 Y2 Y3]T. Find
the matrix A such that u Y=AY. b. Find the covariance matrix of Y and the cross—covariance matrix of X and ”if. c. Find the constants a, b, and c that minimize E[(X — 41171 — bié — c192].

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