Syllabus: STAT 472, STAT 572.

Instructor: Haiming Zhou.

Email: zhouh@niu.edu.

Office Hours: MWF 1-2pm, and by appointment.

Office: DuSable Hall 359E.

Class Meetings: MWF 11-11:50am, DuSable Hall 474.

Textbook: *Mathematical Statistics with Applications, 7th Edition*, by Wackerly, D., Mendenhall, W., and Scheaffer, R. (2008).

- Review: Chapters 2-5.
- Chapter 6: Functions of Random Variables.
- Chapter 7: Sampling Distributions and the Central Limit Theorem, part 1, part 2.
- Chapter 8: Estimation, part 1, part 2.
- Chapter 9: Properties of Point Estimators and Methods of Estimation, part 1, part 2.
- Chapter 10: Hypothesis Testing, part 1, part 2.

- Homework 1: 6.2, 6.4(a), 6.13, 6.15, 6.24, 6.26(a), 6.27(a), 6.28. It is due in class on Wednesday, 1/31/2018.
*Solution*. - Homework 2: 6.43, 6.52, 6.59, 6.60, 6.68, 6.72, 6.78. It is due in class on Wednesday, 2/7/2018.
*Solution*. - Homework 3: 7.11, 7,12, 7.19, 7.20, 7.36, 7.37, 7.38, 7.42, 7.56, 7.73. It is due in class on Friday, 2/16/2018.
*Solution*. - Homework 4: 8.8, 8.10, 8.13, 8.40, 8.41, 8.44, 8.45, 8.47, 8.56, 8.66. It is due in class on Monday, 3/5/2018.
*Solution*. - Homework 5: 8.70, 8.74, 8.82, 8.90, 8.97, 8.102, 9.6, 9.8. It is due in class on Wednesday, 3/21/2018.
*Solution*. - Homework 6: 9.37, 9.38, 9.44, 9.49, 9.54, 9.59, 9.61, 9.65. It is due in class on Friday, 3/30/2018.
*Solution*. - Homework 7: 9.69, 9.72, 9.78, 9.82, 9.83, 9.84, 9.88, 9.96. It is due in class on Wednesday, 4/11/2018.
*Solution*. - Homework 8: 10.2, 10.4, 10.5, 10.19, 10.25. It is due in class on Monday, 4/30/2018.
*Solution*.

- Exam I will be given on Friday (3/2/2018) in class. It covers Chapters 6 and 7. Books, notes or device with internet capability are not allowed. Calculator is allowed, but all memory in the calculator must be cleared before this exam. Formula sheet and scratch paper will be provided during the exam. Here is a set of Practice Problems with the Formula Sheet at the end.
*Solution* - Exam II will be given on Friday (4/20/2018) in class. It covers Chapters 8 and 9.1-9.2, 9.4-9.7. Books, notes or device with internet capability are not allowed. Calculator is allowed, but all memory in the calculator must be cleared before this exam. Formula sheet and scratch paper will be provided during the exam. Here is a set of Practice Problems with the Formula Sheet at the end.
*Solution* - Final Exam will be given on Wednesday (5/9/2018),
**10:00-11:50AM**in the same classroom. It covers Chapters 6, 7, 8, 9 and 10.1-10.3. Books, notes or device with internet capability are not allowed. Calculator is allowed, but all memory in the calculator must be cleared before this exam. Formula sheet and scratch paper will be provided during the exam. Here is a set of Practice Problems with the Formula Sheet at the end. Solution has been given in class; no written solution will be given.

- To install R, go to this website: https://www.r-project.org/ and follow the instructions there.
- Chapter 6: R code for generating random variables from a given CDF.
- Chapter 7: R code for Normal, Chi-squared, t, and F distributions.
- Chapter 8: R code for checking the coverage of a confidence interval.
- Chapter 9: R code for finding MLE numerically.

- The probability distribution of the sum of two independent random variables is the convolution of their individual distributions.
- A complete proof on Independence of Sample Mean and Sample Variance by Prof. Joshua Tebbs: pdf (p. 146-148).
- Some theorems about sample median by Steven Miller: pdf.