Question: Assume that X = Y + 2Z + Y^ 2 where Y and Z are continuous iid random variables and uniformly distributed on [-1, 1]

Assume that X = Y + 2Z + Y^2 where Y and Z are continuous iid random variables and uniformly distributed on [-1, 1]

(a) Find L[X|Y].

(b) Let Q[X|Y] be the quadratic least squares estimate of X given Y , i.e. Q[X|Y] is in the form aY^2+ bY + c. Find Q[X|Y].

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