Problem 30 Random variable X has mean y and variance 202. Three measurements of X are taken: X + 21, Y1 X + Z2 and Y3 X

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Problem 30 Random Variable X Has Mean Y And Variance 202 Three Measurements Of X Are Taken X 21 Y1 X Z2 And Y3 X 1 (65.47 KiB) Viewed 34 times

Problem 30 Random variable X has mean y and variance 202. Three measurements of X are taken: X + 21, Y1 X + Z2 and Y3 X + 23 Y 02 302 9 Variables X, 21, 22 and 23 are assumed uncorrelated. The mean of each Z; equals zero, while Var[21] Var[22] 202 and Var[23] (i) (5 pts.) Determine Cov(X,Y) and Cov(Yi,Y;) for all i and j. (ii) (2 pts.) Determine the linear MMSE estimate of X given Yį and the resulting MMSE. (iii) (3 pts.) Determine the linear MMSE estimate of X given (Y1, Y2) and the resulting MMSE. (iv) (4 pts.) Determine the linear MMSE estimate of X given (Yı, Y2, Y3) and the resulting MMSE. (v) (3 pts.) Determine the linear MMSE estimate of X given S = Y; +Y2 + Y3 and the resulting MMSE. (vi) (3 pts.) Determine the linear MMSE estimate of Yı given (X, Y2, Yz) and the resulting MMSE. Explain the special form of the solution. Notation: You may use Ê[VIO] for the linear MMSE estimate of ♡ given O.