Let (X_{1}, ldots, X_{n}) be a set of independent and identically distributed random variables from a (mathrm{N}(theta,
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Let \(X_{1}, \ldots, X_{n}\) be a set of independent and identically distributed random variables from a \(\mathrm{N}(\theta, 1)\) distribution.
a. Find the maximum likelihood estimator for \(\theta\).
b. Determine whether the maximum likelihood estimator is consistent and asymptotically efficient.
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