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A random sample X1 X2 Xn of size

A random sample X1, X2, ... , Xn of size n is taken from N( μ, σ2), where the variance θ = σ2 is such that 0 < θ < ∞ and μ is a known real number. Show that the maximum likelihood estimator for θ is

and that this estimator is an unbiased estimator of θ.

and that this estimator is an unbiased estimator of θ.

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