# t2 - Stat 5102 Second Midterm Exam Name April 7 2010...

This preview shows pages 1–4. Sign up to view the full content.

Stat 5102 Second Midterm Exam April 7, 2010 Name Student ID The exam is closed book and closed notes. You may use one 8 1 2 × 11 sheet of paper with formulas, etc. You may also use the handouts on “brand name distributions” and Greek letters. Put all of your work on this test form (use the back if necessary). Show your work or give an explanation of your answer. No credit for numbers with no indication of where they came from. IID means independent and identically distributed; PDF means proba- bility density function; MLE means maximum likelihood estimate. The points for the questions total to 100. There are 6 pages and 5 prob- lems. 1. [20 pts.] Suppose X 1 , ... , X n are IID N (0 ), where ν is an unknown parameter satisfying ν > 0. (a) Find the log likelihood for ν . (b) Find the MLE for ν . 1

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

View Full Document
(c) Show that your MLE is a local maximizer of the log likelihood. 2
2. [20 pts.] Suppose X 1 , ... , X n are IID having PDF f θ ( x ) = θ ( θ + 1) x θ - 1 (1 - x ) , 0 < x < 1 where

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 10/28/2010 for the course STAT 5102 taught by Professor Staff during the Spring '03 term at Minnesota.

### Page1 / 6

t2 - Stat 5102 Second Midterm Exam Name April 7 2010...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online