## Math 494 Schedule and Homework - Spring 2018

This a temporary schedule and will be updated as the semester goes.
Week Topic Reading Homework and Exam Handout
Week 1
MLK , 01/17 , 01/19
Review of MGFs, Normal distributions, Student's T-distribution Chapter 3.5-3.6 Placement Exam Introduction to R (Sample codes: P82-84)
Random Number and Special Distributions
Bivariate Normal Distributions
Week 2
01/22, 01/24 , 01/26
Introduction to statistical inference: estimation
Chapter 4.1 HW1: solution
3.5.22, 3.6.4, 3.6.5,
3.6.10, 3.6.14
Introduction to Statistical Inference
Week 3
01/29, 01/31, 02/02
Confidence intervals, Chapter 4.2, 4.3 HW2: solution
4.1.2, 4.1.6, 4.1.8,
4.1.9, 4.2.5, 4.2.9
Demonstration of CI in Poisson Model
Week 4
02/05, 02/07, 02/09
Hypothesis testing (Z-test, t-test),
F-tests,
Chapter 4.5 4.6, 4.7, HW3:solution
4.2.7+4.2.16, 4.2.10,4.2.11,
4.2.18, 4.2.19, 4.2.21
Week 5
02/12, 02/14, 02/16
Chi-square tests,
Chapter 4.4, 4.8 HW4 attached solution Chi-square test
Week 6
02/19, 02/21, 02/23
Order statistics,
Review for Midterm I,
Monte Carlo and Bootstrap procedures
Chapter 4.9 Suggested problems for 4.7, 4.4:
4.7.7, 4.7.9, 4.7.5,
4.4.5, 4.4.22, 4.4.23, 4.4.29, 4.4.30
solution
Midterm I solution
Past Midterm and Solution
Week 7
02/26, 02/28, 03/02
Convergence in probability,
Convergence in distribution,
Law of Large Number (LLN)
Chapter 5.1, 5.2, 5.3 HW 5: 4.7.4, 4.7.6;
4.4.8, 4.4.28, 4.4.32+ QQplots for two datasets
Monte Carlo Methods
MC R codes
Slides on Convergency
Week 8
03/05, 03/07 , 03/09
Law of Large Number (LLN),
Central Limit Theorem (CLT),
Delta method
Chapter 6.1, 6.2 HW6 attached solution Annotated Notes on Convergency
Week 9
Spring Break
Week 10
03/19, 03/21 , 03/23
MLE: Bias, Variance, MSE
Asymptotic properties of MLE
Rao-Cramer lower bound
Chapter 6.3-6.4 HW7: solution
5.2.3, 5.2.8, 5.2.18,
5.3.4, 5.3.11, 5.3.12
Slides on MLE
Week 11
03/26, 03/28 , 03/30
Likelihood Ratio Tests, Score Tests and Wald Tests,
Review for Midterm II, EM-algorithm
Chapter 6.5 HW8: solution
6.1.2, 6.1.5, 6.1.6,
6.2.7, 6.2.10, 6.2.11,
Annotated Notes on MLE
Week 12
04/02, 04/04 , 04/06
Sufficient statistics,
Factorization Theorem,
Chapter 7.2 Suggested problems: solution part 1 part 2
6.3.1, 6.3.8, 6.3.9, 6.3.10 ,6.3.12, 6.3.16, 6.3.16
Past exams 1 2
Midterm II solution
Slides on Sufficiency
Week 13
04/09, 04/11 , 04/13
Minimal sufficiency and ancillary statistics,
Complete statistics, Basu's Theorem,
Exponential family of distributions
Chapter 7.8, 7.4, 7.9, 7.5 HW9 attached : solution Annotated Notes on Sufficiency
Week 14
04/16, 04/18 , 04/20
Rao-Blackwell Theorem, Lehman and Scheffe Theorem,
UMVUE
Chapter 7.5 -7.7, 7.1, 7.3 HW10: solution
7.8.1, 7.9.2, 7.9.6, 7.5.5, 7.5.6, 7.5.11
Slides on UMVUE and UMP
Week 15
04/23, 04/25 , 04/27
UMP,
UMPU,
Review
Chapter 8.1-8.3 HW11: solution
7.4.9, 7.5.12, 7.6.5, 7.7.5, 8.1.7,8.2.12 8.3.12
Annotated Notes on Optimal Estimation and Test
Final Week 05/07   Final Exam: Solution
Take Home Exam : Solution
Past Finals 1 2

• Reading and Problems in text are from
Hogg, McKean & Craig, Introduction to Mathematical Statistics , 7th.
• Relationships among common distributions
• Table of common distributions
• Table of common distributions in Appendix D
• Tables of Normal, t, and Chi-square distributions
• Tables of F distribution