Question: X is a 3-dimensional random vector with E[X] = 0 and autocorrelation matrix R x with elements R X (i,j) = 1 0.25|i

X is a 3-dimensional random vector with E[X] = 0 and autocorrelation matrix Rx with elements

RX(i,j) = 1 – 0.25|i – j|.


Y is a two-dimensional random vector with

Y1 = X1 + X2, Y2 = X2 + X3.

Use Y to form X1 = [a1 . a2] Y, a linear estimate of X1.

(a) Find the optimum coefficients a1 and a2 and the minimum mean square error e*L.

Use Y1 to form a linear estimate of X1: X1 = aY1 + b.. What are the optimum coefficients a* and b*? What is the minimum mean square error e*L?

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