{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Stat400Lec17(Ch6.1) - STAT 400 p.m.f or p.d.f(Chapter 6.1 f...

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

View Full Document Right Arrow Icon
STAT 400 (Chapter 6.1) Spring 2012 p.m.f. or p.d.f. f ( x ; ) , . parameter space. 1. Suppose = { 1, 2, 3 } and the p.d.f. f ( x ; ) is = 1: f ( 1 ; 1 ) = 0.6, f ( 2 ; 1 ) = 0.1, f ( 3 ; 1 ) = 0.1, f ( 4 ; 1 ) = 0.2. = 2: f ( 1 ; 2 ) = 0.2, f ( 2 ; 2 ) = 0.3, f ( 3 ; 2 ) = 0.3, f ( 4 ; 2 ) = 0.2. = 3: f ( 1 ; 3 ) = 0.3, f ( 2 ; 3 ) = 0.4, f ( 3 ; 3 ) = 0.2, f ( 4 ; 3 ) = 0.1. What is the maximum likelihood estimate of ( based on only one observation of X ) if … a) X = 1; b) X = 2; c) X = 3; d) X = 4. Likelihood function: L ( ) = L ( ; x 1 , x 2 , … , x n ) = n i 1 f ( x i ; ) = f ( x 1 ; ) f ( x n ; ) It is often easier to consider ln L ( ) = n i 1 ln f ( x i ; ) . The maximum likelihood estimator (MLE) is the value that maximize the (log) likelihood function.
Background image of page 1

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

View Full Document Right Arrow Icon
1½. Let X 1 , X 2 , … , X n be a random sample of size n from a Poisson distribution with mean , > 0. a) Obtain the maximum likelihood estimator of , ˆ . Let θ ˆ be the maximum likelihood estimate (m.l.e.) of . Then the MLE of any function h ( ) is h ( θ ˆ ) . ( The Invariance Principle ) b) Obtain the maximum likelihood estimator of P ( X = 2 ) .
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}