# 409Hw11 - STAT 409 Homework #11 Fall 2009 (due Wednesday,...

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

Homework #11 Fall 2009 (due Wednesday, November 13, by 4:00 p.m.) 1. Let λ > 0 and let X 1 , X 2 , … , X n be independent random variables, each with the probability density function f ( x ) = < + 1 0 1 1 λ λ x x x . We wish to test H 0 : λ = 1 vs. H 1 : λ > 1. a) Find a sufficient statistic for λ . b) Find a uniformly most powerful rejection region. That is, find a rejection region that is most powerful for testing H 0 : λ = 1 vs. H 1 : λ = λ 1 for all λ 1 > 1. Hint: It should look like “Reject H 0 if Y c or “Reject H 0 if Y c ”, where Y = u ( X 1 , X 2 , … , X n ) is a sufficient statistic for λ . 2. 1. (continued) Let X 1 , X 2 be a random sample of size n = 2 from a probability distribution with p.d.f. f ( x ). c) Sketch a typical rejection region obtained in part 1 (a). Hint: Recall that x 1 1, x 2 1, so c > 1 ( if you are using = n i i x 1 ). d)

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

View Full Document
This is the end of the preview. Sign up to access the rest of the 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.

### Page1 / 2

409Hw11 - STAT 409 Homework #11 Fall 2009 (due Wednesday,...

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

View Full Document
Ask a homework question - tutors are online