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6.4-2. A random sample X₁, X2,..., Xn of size n is taken from N(μ, o²), where the variance 0 = o² is such that 0 < 0 <∞ and μ is a known real number. Show that the maxi- mum likelihood estimator for is@= (1/n) 1 (X₁-μ)² and that this estimator is an unbiased estimator of 0.

6.4-2. A random sample X₁, X2,..., Xn of size n is taken from N(μ, o²), where the variance 0 = o² is such that 0 < 0 <∞ and μ is a known real number. Show that the maxi- mum likelihood estimator for is@= (1/n) 1 (X₁-μ)² and that this estimator is an unbiased estimator of 0.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 29E
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6.4-2. A random sample X₁, X2,..., Xn of size n is taken from N(μ, o²), where the variance 0 = o² is such that 0 < 0 <∞ and μ is a known real number. Show that the maxi- mum likelihood estimator for is@= (1/n) 1 (X₁-μ)² and that this estimator is an unbiased estimator of 0.
Transcribed Image Text:6.4-2. A random sample X₁, X2,..., Xn of size n is taken from N(μ, o²), where the variance 0 = o² is such that 0 < 0 <∞ and μ is a known real number. Show that the maxi- mum likelihood estimator for is@= (1/n) 1 (X₁-μ)² and that this estimator is an unbiased estimator of 0.
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