(Solution) - Suppose that Yi Xi satisfy the assumptions in Key Concept -(2025 Original AI-Free Solution)

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Suppose that (Yi, Xi) satisfy the assumptions in Key Concept 4.3 and, in addition, ui is N(0, ?2u) and is independent of Xi.
(a) Is pi conditionally unbiased?
(b) Is pi the best linear conditionally unbiased estimator of 1?
(c) How would your answers to (a) and (b) change if you assumed only that (Yi, Xi) satisfied the assumptions in Key Concept 4.3 and var(uiXi = x) is constant?
(d) How would your answers to (a) and (b) change if you assumed only that (Yi, Xi) satisfied the assumptions in Key Concept 4.3?