Math 5080: Statistical Inference I

Math 5080: Statistical Inference I. Spring '10

Schedule: Meets MW 6:00--7:30pm LCB 222.

Instructor: Stewart Ethier (Prof.), JWB 119, 581-6148, ethier@math.utah.edu. Office hours 11:00--12:00 MWF. Other times are available by appointment.

Prerequisite: Math 5010, Introduction to Probability. (This is essential!)

Text: Introduction to Probability and Mathematical Statistics, 2nd Ed., by Bain and Engelhardt.

Topics covered: Estimation theory. We will review some probability topics (Chapters 6 and 7) and cover sampling distributions, point estimation, sufficiency and completeness, and interval estimation (Chapters 8-11). Math 5090 will deal with hypothesis testing.

Homework and quizzes: An assignment from the text will be given each week after Wednesday's class based on that week's material and posted on this web page. You should attempt a solution to prepare for the 15-minute quiz the following Wednesday. Solutions will be posted by Tuesday afternoon. There will be 11 quizzes during the semester. To allow for occasional illnesses and absences, you need only turn in 8 quizzes of the 11. Every quiz that is turned in will count in your average. If you feel you did poorly on a quiz, you needn't turn it in, but if you do turn it in, it will count. Make-up quizzes will not be given.

Grades: Grades will be based on your quiz average (20%), two midterm exams (25% each), and a final exam (30%). The dates of the midterms will be announced at least a week in advance and posted on this page (probably the 6th and 12th weeks). The final exam is scheduled for Monday, May 3, 6:00-8:00pm.

Week 1 (Jan. 11, 13). We covered Sections 6.2 and 6.3 through page 204. Assignment 1. Chapter 6, Exercises 2, 4, 9, 10, 13. Solutions.
Week 2 (Jan. 20). We finished Section 6.3. Assignment 2. Chapter 6, Exercises 14, 16, 17, 18. Solutions.
Week 3 (Jan. 25, 27). We nearly finished Chapter 6 (we will omit the section on censored sampling). Assignment 3. Chapter 6, Exercises 23, 25, 27, 28, 29, 31. Solutions.
Week 4 (Feb. 1, 3). We covered through Section 7.5. (We didn't discuss Section 7.4 explicitly because that is review.) Assignment 4. Chapter 7, Exercises 1, 2, 3, 7, 15. Solutions.
Week 5 (Feb. 8, 10). We finished Chapter 7 (with light coverage of Section 7.8) and got through Section 8.2. Assignment 5. Chapter 7, Exercises 16, 17. Solutions.
Week 6 (Feb. 17). We covered most of Sections 8.3 and 8.4, emphasizing the definitions of the chi squared, t, and F distributions. Assignment 6. Chapter 8, Exercises 13, 15. Solutions.
Week 7 (Feb. 22, 24). We nearly finished Chapter 8, getting through page 277. We also had Exam 1. Solutions. Assignment 7. Chapter 8, Exercises 8, 9, 11, 12, 17, 18. Solutions.
Week 8 (Mar. 1, 3). We nearly finished Section 9.2. Assignment 8. Chapter 9, Exercises 1--4. Solutions.
Week 9 (Mar. 8, 10). We continued with Chapter 9, getting to about page 307. Assignment 9. Chapter 9, Exercises 5, 6, 7, 9, 10, 13, 17, 19, 21, 23, 26. Solutions.
Week 10 (Mar. 15, 17). We nearly finished Chapter 9. Assignment 10. Chapter 9, Exercises 28, 31, 33, 34, 44. Solutions.
Week 11 (Mar. 29, 31). We got as far as page 343. Assignment 11. Chapter 10, Exercises 2, 3, 9, 12, 13, 14. Solutions.
Week 12 (Apr. 5, 7). We finished Chapter 10 except for Basu's theorem. Assignment 12. Chapter 10, Exercises 17, 18, 20, 21, 24, 25, and prepare for Exam 2. Solutions.
Week 13 (Apr. 12, 14). We started Chapter 11, getting to page 363. We also had Exam 2. Solutions. Assignment 13. Chapter 11, Exercises 1, 2, 3, 5, 6, 7. Solutions.
Week 14 (Apr. 19, 21). We finished Section 11.4. Assignment 14. Chapter 11, Exercises 8, 10, 11, 13, 15. Solutions.
Week 15 (Apr. 26, 28). We finished Section 11.5 and reviewed. Assignment 15. Chapter 11, Exercises 19, 20, 25. Solutions. Topics to be reviewed for final exam here. Practice final exam here. Solutions here.

For more information on the theorems of Section 11.3, see Bain.