4.37 Consider the same model as in the preceding problem.

(a) Prove the optimal smoothed estimator of the form

(c) Compare mean square error of the estimator in part

(b) with that of the optimal finite estimator of the form xt = a1yt−1 + a2yt−2 when σ2 v = .053, σ2w = .172, and φ1 = .9.

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has I = asyt-s x-=8 02 00 ag= 021-02 (b) Show the mean square error is given by 0202 E{(xt-t)} = (1-0)