hw3 stat practice

hw3 stat practice - STAT 409 Homework #3 Fall 2008 (due...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: STAT 409 Homework #3 Fall 2008 (due Friday, September 19, by 4:00 p.m.) 1. Let X 1 , X 2 , , X n be a random sample from the distribution with probability density function a) ( ) 3 2 & 3 & x e x x f- = x > 0 > 0. Find the sufficient statistic Y = u ( X 1 , X 2 , , X n ) for . f ( x 1 , x 2 , x n ; ) = f ( x 1 ; ) f ( x 2 ; ) f ( x n ; ) = & & = =- n i i x n n x n i i e 1 2 1 3 & 3 & . By Factorization Theorem, Y = = n i i 1 3 X is a sufficient statistic for . OR f ( x ; ) = { } 3 ln ln ln exp 2 3 & & x x + + +- . K ( x ) = x 3 . Y = = n i i 1 3 X is a sufficient statistic for . b) ( ) ( ) ( ) 1 1 2 & & & x x x f- + =- 0 < x < 1 > 0. Find the sufficient statistic Y = u ( X 1 , X 2 , , X n ) for . f ( x 1 , x 2 , x n ; ) = f ( x 1 ; ) f ( x 2 ; ) f ( x n ; ) = ( ) ( ) =- =- & & + n i i n i i n x x 1 1 1 2 1 & & & . By Factorization Theorem, Y = = n i i 1 X is a sufficient statistic for . OR f ( x ; ) = ( ) ( ) ( ) { } 2 1 1 ln & & ln ln & exp x x- + + +- . & K ( x ) = x ln . & Y = ( ) = n i i 1 X K = = n i i 1 X ln is a sufficient statistic for . 2. Let X 1 , X 2 , , X n be a random sample of size n from the distribution with probability density function ( ) ( ) ( ) & 2 X X ln 1 & & ; x x x f x f - = = , x > 1, > 1....
View Full Document

Page1 / 9

hw3 stat practice - STAT 409 Homework #3 Fall 2008 (due...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online