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409Hw03 - STAT 409 Homework#3 Fall 2009(due Friday...

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Unformatted text preview: STAT 409 Homework #3 Fall 2009 (due Friday, September 18, by 4:00 p.m.) 1. Let X 1 , X 2 , … , X n be a random sample of size n from the distribution with probability density function ( 29 ( 29 ( 29 θ 2 X X ln 1 θ θ ; x x x f x f ⋅- = = , x > 1, θ > 1. a) Find the sufficient statistic Y = u ( X 1 , X 2 , … , X n ) for θ . b) What is the probability distribution of W = ln X ? c) What is the probability distribution of ∑ = n i i 1 X ln ? 2. Let X 1 , X 2 , … , X n be a random sample from the distribution with probability density function ( 29 ( 29 X X θ 2 θ θ ; x e x x f x f- = = x > 0 θ > 0. a) Find the sufficient statistic Y = u ( X 1 , X 2 , … , X n ) for θ . b) What is the probability distribution of W = X ? c) What is the probability distribution of ∑ = n i i 1 X ? 3. Let X 1 , X 2 , … , X n be a random sample of size n from a shifted Exponential ( 1 ) distribution with probability density function ( 29 ( 29 ( 29 θ X X θ ;-- = = x e x f x f , x > θ , θ ∈...
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409Hw03 - STAT 409 Homework#3 Fall 2009(due Friday...

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