409Quiz1Fans - x ) = x 3 . Y = ( ) = n i i 1 X K = = n i i...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
STAT 409 Fall 2011 Version F Name ANSWERS . Quiz 1 (10 points) Be sure to show all your work, your partial credit might depend on it. No credit will be given without supporting work. 1. Let X 1 , X 2 , … , X n be a random sample from the distribution with probability density function ( ) 3 τ 8 14 5 X τ τ ; x e x x f - = , x > 0, τ > 0. a) (3) Find a sufficient statistic Y = u ( X 1 , X 2 , … , X n ) for τ . f ( x 1 , x 2 , x n ; τ ) = f X ( x 1 ; τ ) f X ( x 2 ; τ ) f X ( x n ; τ ) = = = - n i i x n n x n i i e 1 14 5 τ 8 1 3 τ . By Factorization Theorem, Y = = n i i 1 3 X is a sufficient statistic for τ . OR f X ( x ; τ ) = { } 3 n ln ln exp l 14 8 5 τ τ x x + - + - . K (
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x ) = x 3 . Y = ( ) = n i i 1 X K = = n i i 1 3 X is a sufficient statistic for . b) (7) Obtain the maximum likelihood estimator of , . L ( ) = =- n i x i i e x 1 14 5 3 8 = =- = n i i x n i i n n e x 1 14 5 1 3 8 ln L ( ) = = = -+-n i i n i i x x n n 1 3 1 14 8 5 ln ln ln ( ln L ( ) ) ' = =-n i i x n 1 3 5 = 0 = = n i i n 1 3 X 5 ....
View Full Document

This note was uploaded on 09/14/2011 for the course STAT 409 taught by Professor Stephanov during the Fall '11 term at University of Illinois at Urbana–Champaign.

Page1 / 2

409Quiz1Fans - x ) = x 3 . Y = ( ) = n i i 1 X K = = n i i...

This preview shows document pages 1 - 2. Sign up to view the full document.

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