Instructor: Yizhe Zhu, yizhezhu@usc.edu
Instructor Office Hours: Monday 9-10 am at KAP 464B and Thursday 4-5 pm on Zoom via this link
TA: Robin Rong, zijianro@usc.edu
TA Office Hours: Wednesday 12 pm-1 pm and Thursday 10 am-12 pm at the math center (KAP 263)
Class schedule: MWF 11:00-11:50 am at ZHS 163
Prerequisite: Math 407 Probability Theory
Course Description: This is an introductory course to mathematical statistics for undergraduate students.
Topics: We plan to cover Chapters 8-16 of the textbook: Estimation, Properties of Point Estimators and Methods of Estimation, Hypothesis Testing, Linear Models and Estimation by Least Squares, The Analysis of Variance, Analysis of Categorical Data, Non-parametric Statistics, Introduction to Bayesian Methods for Inference.
Textbook: Wackerly, Dennis D., William Mendenhall, and Richard L. Scheaffer. Mathematical statistics with applications. 7th Edition.
Exam dates:
Midterm 1: Wednesday, Feb 25, 11:00-11:50 am, ZHS 163
Midterm 2: Wednesday, April 15, 11:00-11:50 am, ZHS 163
Final: Wednesday, May 6, 11 am-1 pm, ZHS 163
Homework: Homework will be posted on Brightspace
Quiz: Quizzes are on weeks 3,5,8,11,13,15 during discussion.
Course Schedule: Below is a tentative schedule, to be updated as the semester progresses.
Week 1
January 12: Point estimators, bias and variance decomposition, mean squared error
January 14: Examples of point estimators
January 16: Confidence interval
Week 2
January 19: No class
January 21: Large sample confidence intervals
January 23: Relative efficiency of point estimators
Week 3
January 26: Consistency
January 27: Quiz 1
January 28: CLT with sample variance, sufficiency
January 30: Sufficiency, the Rao-Blackwell Theorem
Week 4
February 2: The Rao-Backwell Theorem and Minimum-Variance Unbiased Estimator
February 4: Minimal sufficient statistic, MVUE
February 6: Method of Moments, Maximum Likelihood Estimation
Week 5
February 9: Method of Maximum Likelihood
February 10: Quiz 2
February 11: Elements of a statistical test
February 13: Common Large-Sample Tests
Week 6
February 16: No class
February 18: Calculating Type II error probabilities and finding the sample size for Z tests
February 20: p-values
Week 7
February 23: Power of a test
February 25: Midterm 1
February 27: Neyman-Pearson lemma
Week 8
March 2: Linear statistical models, least squares solution
March 3: Quiz 3
March 4: Properties of the least squares solution
March 6: Properties of the least squares solution
Week 9
March 9: estimating the variance, chi-squared distribution
March 11: Student's t-distribution, inferences concerning the parameters
March 13: linear functions of the model parameters
Week 10
March 16: No class
March 18: No class
March 20: No class
Week 11
March 23: Predicting a Particular Value using simple linear regression
March 24: Quiz 4
March 25: Correlation coefficient
March 27: Fitting the linear model using matrices
Week 12
March 30: Properties of the least squares solution: multiple linear regression
April 1: Analysis of Variance for a One-Way Layout
April 3: F test for ANOVA
Week 13
April 6: ANOVA and multiple linear regression
April 7: Quiz 5
April 8: Categorical data and multinomial distribution
April 10: The chi-squared test
Week 14
April 13: Review (Zoom recording)
April 15: Midterm 2
April 17: Contingency tables, test of independence
Week 15
April 20: Bayes' rule, prior, posterior
April 21: Quiz 6
April 22: Conjugate family
April 24: Bayesian estimators and Bayesian credible interval
Week 16
April 27: Bayesian hypothesis testing
April 29: Review
May 1: Review and sample problem sets