Let be iid observations from , is known and is an unknown real number. Let be the paramete...

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Let X_1, X_2,...,X_n be iid observations from $σ2 (μ, )$ , $\sigma ^{2}>0$ is known and $\mu$ is an unknown real number. Let $g(t) = 211$ be the parameter of interest.

(a) Find the CRLB for the variance of an unbiased estimator for $g( \mu )$ .

(b) Find the UMVUE for $g( \mu )$ .

(c) Show that $T(X_1,...,X_n) =X_{1}^{2} + 2X_{3} - X_{4}^{2}$ is an unbiased estimator for $g( \mu )$ .

(d) Show that $E(T|\bar{X}) = 2\bar{X}$ .

σ2 (μ, )

g(t) = 211

math Statistics-And-Probability

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Let be iid observations from , is known and is an unknown real number. Let be the paramete...

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