# 09_09_09 - STAT 409 Def Examples for Fall 2009 Let X 1 X 2...

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

STAT 409 Examples for 09/09/09 Fall 2009 Def Let X 1 , X 2 , … , X n denote random variables with joint p.d.f. or p.m.f. f ( x 1 , x 2 , , x n ; θ ) , which depends on the parameter θ . The statistic Y = u ( X 1 , X 2 , , X n ) is said to be sufficient for θ if the conditional distribution of X 1 , X 2 , … , X n given Y = y is independent of θ for all y . Theorem 1 ( Factorization Theorem ) : Let X 1 , X 2 , … , X n denote random variables with joint p.d.f. or p.m.f. f ( x 1 , x 2 , , x n ; θ ) , which depends on the parameter θ . The statistic Y = u ( X 1 , X 2 , , X n ) is sufficient for θ if and only if f ( x 1 , x 2 , , x n ; θ ) = φ [ u ( x 1 , x 2 , , x n ) ; θ ] h ( x 1 , x 2 , , x n ) , where depends on x 1 , x 2 , , x n only through u ( x 1 , x 2 , , x n ) and h ( x 1 , x 2 , , x n ) does not depend on θ . 1. Let X 1 , X 2 , … , X n be a random sample of size n from a Poisson distribution with mean λ . That is,

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.

{[ snackBarMessage ]}

### Page1 / 2

09_09_09 - STAT 409 Def Examples for Fall 2009 Let X 1 X 2...

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

View Full Document
Ask a homework question - tutors are online