This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Stat 411 Homework 04 Solutions 1. Problem 6.2.7 in the text . The PDF for the Gamma (4 , ) distribution is f ( x ) = 1 6 4 x 3 e x/ , x > , > . (a) For the Fisher information, we first need second derivative of logPDF: 2 2 log f ( x ) = 2 2 h const 4 log  x i = 4 2 2 x 3 . If we recall that the expected value of a Gamma ( , ) random variable is (see middle of p. 151 in the text), then I ( ) = E h 2 2 log f ( X ) i = E (2 X ) 3 4 2 = 2 4 2 4 2 = 4 2 . (b) If X 1 ,...,X n iid Gamma (4 , ), then the MLE is found by maximizing the log likelihood: ( ) = log L ( ) = const 4 n log  n x/. Setting the derivative equal to zero and solving for gives: ( ) = 4 n + n x 2 set = 0 = x 4 . If we recall that the variance of a Gamma ( , ) random variable is 2 (see middle of p. 151 in the text), then V ( ) = V ( X 1 ) 16 n = 4 2...
View
Full
Document
This note was uploaded on 03/12/2012 for the course STAT 411 taught by Professor Staff during the Spring '08 term at Ill. Chicago.
 Spring '08
 STAFF

Click to edit the document details