For the simple regression model yi = + i, i ~ N [0, 2], prove that

Question:

For the simple regression model yi = μ + εi, εi ~ N [0, σ2], prove that the sample mean is consistent and asymptotically normally distributed. Now consider the alternative estimator μ = Σi wi yi, wt = 1/(n(n+1)/2) = i/Σi i. Note that Σi wi = 1. Prove that this is a consistent estimator of μ and obtain its asymptotic variance.