Let Xâ‚, Xâ‚‚, ..., Xâ‚™ be a random sample from a normal distribution with mean μ and known variance σ². Find the UMVU estimator of μ.
Added by Jordan P.
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Step 1
First, we need to find the maximum likelihood estimator (MLE) of μ. Since Xi ~ N(μ, σ^2), the likelihood function is: L(μ; x1, x2, ..., xn) = (2πσ^2)^(-n/2) exp[-(1/2σ^2)Σ(xi-μ)^2] Taking the derivative of the log-likelihood function with respect to μ and Show more…
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