# Let X1, X2, and X3 be a random sample of size n = 3 from a probability distribution with mean µ and.

Let X1, X2, and X3 be a random sample of size n = 3 from a probability distribution with mean µ and.
Let X1, X2, and X3 be a random sample of size n = 3 from a probability
distribution with mean μ and variance σ2. For a ∈ [0,2/3], let δa =
δa(X1,X2,X3) be an estimator of μ: ) Show that δa is an unbiased estimator of μ for each a ∈[0,2/3].
(b) Derive the variance of δa.
(c) Show that δ1/3 is the most efficient estimator within this class
of estimators. That is, the variance in Part (b) is minimized by
a = 1/3. May 11 2022 01:56 AM

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