Yk q0 q1k q2k2 Zk, Where q 0 q 1 k q 2 k 2 is an unknown quadratic function of k and Z k is a sequence of iid Gaussian (0,1) noise random variables We wish to estimate the unknown parameters q 0 , q 1 , and q 2 of the quadratic function Suppose we assume q 0 , q 1 , and q 2 are samples of iid Gaussian (0,1) random variables Find the optimum linear estimator Q(Y) of Q q 0 q 1 q 2 ' given the ovservation Y Y 1 Y n

Question: Yk = q0 + q1k + q2k2 + Zk, Where q 0 + q 1 k + q 2 k 2 is an unknown quadratic

Yk = q0 + q1k + q2k2 + Zk,

Where q₀ + q₁k + q₂k² is an unknown quadratic function of k and Z_k is a sequence of iid Gaussian (0,1) noise random variables. We wish to estimate the unknown parameters q₀, q₁, and q₂ of the quadratic function. Suppose we assume q₀, q₁, and q₂ are samples of iid Gaussian (0,1) random variables. Find the optimum linear estimator Q(Y) of Q = [q₀ q₁ q₂]' given the ovservation Y =[Y₁ ∙ ∙ ∙ Y_n] ʹ.

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