This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 ∈...
View
Full
Document
This note was uploaded on 10/12/2011 for the course STATISTICS stat 410 taught by Professor Stepanov during the Spring '11 term at University of Illinois, Urbana Champaign.
 Spring '11
 Stepanov
 Probability

Click to edit the document details