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Hw12 - f x θ = θ x θ – 1 0< x< 1 where θ> 0 a...

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STAT 410 Homework #12 Spring 2008 (due Thursday, April 17, by 5:00 p.m.) 1. 5.7.4 2. 5.7.5 3. 5.7.6 4. Let X 1 , X 2 , … , X n be a random sample of size n from a N ( 0 , σ 2 ) distribution. a) Find the sufficient statistic Y for σ 2 . ( See 7.2.1 . ) b) Show that the maximum likelihood estimator for σ 2 is a function of Y . c) Is the maximum likelihood estimator for σ 2 unbiased? 5. Let X 1 , X 2 , … , X n be a random sample of size n from a distribution with p.d.f. f ( x ; θ ) = θ
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Unformatted text preview: f ( x ; θ ) = θ x θ – 1 , 0 < x < 1, where θ > 0. a) Find the sufficient statistic Y for θ . b) Show that the maximum likelihood estimator for θ is a function of Y . c) Argue that & ˆ is also sufficient for θ . 6. a) 7.2.4 b) 7.2.7 7. a) 7.2.6 b) 7.2.8 _________________________________________________________________________ If you are registered for 4 credit hours: ( to be handed in separately ) 8. 5.7.9...
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