Math 476: Mathematical Statistics
Homework schedule
Homework assignments will be posted at least one week before the due date. It is your responsibility to check the course page on Piazza, which you can easily access directly or by logging into Blackboard, to obtain the assigned problems.You are expected to start working on the homework sets early (not the day they are due or right before). It is extremely difficult to answer lastminute homework questions; particularly if you have not been participating in the Piazza discussion beforehand.
Help with writing up assignments
[Credit: the text in this paragraph is borrowed from Prof. Kaul.]To improve your mathematical writing quickly, start by writing draft solutions to homework early. A day or two later after you have had time to forget what you wrote, read it. If it doesn’t make sense or convince you, rewrite it. Writing a solution requires saying what you mean and meaning what you say. Be intellectually honest. Intellectual dishonesty includes: 1) stating a “reason” without understanding its relevance. 2) Claiming a conclusion when you know you haven’t proved it. 3) Giving an example and claiming you have proved the statement for all instances.
Lecture schedule
You are expected to cover (at least at a high level) the assigned readings before coming to the lecture. This will help you follow the course and organize your notes. In the reading schedule below, "WMS" refers to Wackerly, Mendhall, Scheaffer, Mathematical Statistics with Applications.Homework problem sets are naturally related to the material covered in the course; hence, homework numbers are listed next to the corresponding topic.
Dates..............  Tentative topics covered  Assigned reading  Related homework 
January 9&11  Topic 1: What is statistical inference? Statistics and sampling distributions  WMS: Sections 1.4, 7.17.4. 
Homework 1 due 1/25. 
January 16&18  Topic 1, continued. Start of Topic 2: Estimation: point estimation basics. Bias. Goodness of a point estimator. 
WMS: Sections 7.17.4. Start of 8.18.4. 
Homework 1 due 1/25. 
January 23&25  Topic 2 (cont'd): Estimation: point estimation basics. Topic 3: Estimation: Conidence intervals and sample size. 
WMS: 8.18.4. WMS: 8.5. 
Homework 2 due 2/1. 
Jan30&Feb1  Topic 3 (cont'd): Estimation: confidence intervals. Some additional examples. 
WMS: 8.58.9 
Homework 3 due 2/8. 
February 6&8  Topic 4 (cont'd): Properties of point estimators: efficincy, consistency, sufficiency.  WMS: 9.19.5.  Homework 4 due 2/15. 
February 13&15  Topic 4 (cont'd): MVUEs. RaoBlackwell. Topic 5: Where do estimators come from? Methods of moments and maximum likelihood; Computing MLEs and examples. 
WMS: 9.7, 9.8, and references given in the book. 
Homework 5 due 
February 20&22  Topic 5 (cont'd): Properties of Maximum likelihood estimators. [invariance, consistency, efficiency, asymptotic normality.] AND: review of Chapters 8 and 9. Topic 6: Introduction to hypethesis testing: Elements of a statistical test; 
Homework 6 due 3/22 (see Piazza!)  
February 27  QUIZ 1: In class, one page of notes allowed. Chapters 8 and 7.  Homework sets 1  3.  
Feb 27 & Mar 1  Topic 6 (cont'd) Common largesample tests. Calculating Type II Error probabilities and finding sample size for Z tests 
WMS: 10.310.5. 
Homework 6 due 3/22 (after spring break). 
MARCH 6th  MIDTERM EXAM: In class, one page of notes allowed.  Chapters 7, 8 and 9.  Homework sets 1  5. 
March 6&8  Tuesday is midterm. Thursday is Topic 7 intro. (see below).  WMS: 10.6, 10.7, 10.8 (and 10.9, time permitting) 
Homework 7 due 3/29 
March 13&15  spring break  Catch up on reading! Work on HW 6!  
March 20&22  Topic 7, continued: pvalues. Small sample tests. Hypothesis testing for variances. 
WMS: 10.9, 10.10, 10.11, 10.12. 
Homework 7 due 3/29 
March 27 & 29  Topic 8: (timepermitting) Power of tests, NeymanPearson, Likelihood ratio tests. 
WMS: 10.12. 
Homework 8 due 4/5 
April 3&5  Topic 8, wrapup: likelihood ratio tests. Topic 9: Analysis of categorical data  an introduction. 
WMS: 14.114.4.  Homework 9 due 
April 10&12  Finished chapter 14, including Fisher's exact test (exact pvalue computation), chisquare test of independence in twoway contingency tables.
Topic 10: linear models. Introduction. 
Haberman 1988, Bunea and Besag 2000. WMS: 11.111.4. 

April 17&19  Topic 10: linear models. Linear statistical models, method of least squares, properites of LS estimators (simple linear regression). 
WMS: 11.111.4  HW 10 TBD. 
(Comprehensive) Final Exam  FRIDAY, May 4th 2018, 24pm. 