(a) Show that T = ) X; is a sufficient statistic. What is the distribution of T? i=1 (b) Find an MLE for 0. (c) Using the distribution of T, argue that the MLE from (b) is the MVUE for 0.

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Let X1, X2,..., X, be a random sample from a population r.v. X - N(0,0²), with o
to be known.
(a) Show that T =X; is a sufficient statistic. What is the distribution of T?
i=1
(b) Find an MLE for 0.
(c) Using the distribution of T, argue that the MLE from (b) is the MVUE for 0.
Transcribed Image Text:Let X1, X2,..., X, be a random sample from a population r.v. X - N(0,0²), with o to be known. (a) Show that T =X; is a sufficient statistic. What is the distribution of T? i=1 (b) Find an MLE for 0. (c) Using the distribution of T, argue that the MLE from (b) is the MVUE for 0.
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