Suppose that Y, Y2, Y3 is a sample of independent observations from a Normal(u,0) population. Consider...

 

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Suppose that Y₁, Y2, Y3 is a sample of independent observations from a Normal(u,0²) population. Consider two estimators for the population mean u. Ỹ = (Y₁ + Y₂ + Y3) and Ỹ = V₁ + ²Y₂ +¹Y3. (a) Explain whether each of them is a linear estimator of μ. (b) Find E(Y) and E(Ỹ). | (c) Find Var(Y) and Var(Y). (d) Graph the sampling distributions of the estimators together on the same diagram, assuming normal distributions. Explain which is a better estimator for u. Suppose that Y₁, Y2, Y3 is a sample of independent observations from a Normal(u,0²) population. Consider two estimators for the population mean u. Ỹ = (Y₁ + Y₂ + Y3) and Ỹ = V₁ + ²Y₂ +¹Y3. (a) Explain whether each of them is a linear estimator of μ. (b) Find E(Y) and E(Ỹ). | (c) Find Var(Y) and Var(Y). (d) Graph the sampling distributions of the estimators together on the same diagram, assuming normal distributions. Explain which is a better estimator for u.