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STAT 330Mathematical Statistics

Units
0.50
Faculty
Mathematics
Subject
Statistics

When it runs

  1. F24
  2. W25
  3. S25
  4. F25
  5. W26
  6. S26
  7. F26
  8. W27
  9. S27

Ran in 7 of the last 7 terms. Winter 2027: scheduled, 3 lecture sections. Spring 2027: schedule not out yet.

This course provides a mathematically rigorous treatment for topics covered in STAT 230 and 231, and to make essential extensions to the multivariate case. Maximum likelihood estimation. Random variables and distribution theory. Generating functions. Functions of random variables. Limiting distributions. Large sample theory of likelihood methods. Likelihood ratio tests. Joint probability (density) functions, marginal probability (density) functions, and conditional probability (density) functions of two or more random variables are discussed. Topics covered include independence of random variables, conditional expectation and the determination of the distribution of functions of random variables using the cumulative distribution method, change of variable and moment generating functions. Properties of the Multinomial and Bivariate Normal distributions are proved. Limiting distributions, including convergence in probability and convergence in distribution, are discussed. Important results, including the Weak Law of Large Numbers, Central Limit Theorem, Slutsky's theorem, and the Delta Method, are introduced with applications. The maximum likelihood method is discussed for the multi-parameter case. Asymptotic properties of the maximum likelihood estimator are examined and used to construct confidence intervals or regions. Tests for simple and composite hypotheses are constructed using the Likelihood Ratio Test.

Prerequisites

  • Complete all of the following
    • Must have completed at least 1 of the following:
      • MATH237 - Calculus 3 for Honours Mathematics (0.50)
      • MATH247 - Calculus 3 (Advanced Level) (0.50)
    • Must have completed at least 1 of the following:
      • STAT231 - Statistics (0.50)
      • STAT241 - Statistics (Advanced Level) (0.50)
    • Complete 1 of the following
      • Must have completed the following:
        • STAT240 - Probability (Advanced Level) (0.50)
      • Earned a minimum grade of 60% in each of the following:

Antirequisites

  • Not completed nor concurrently enrolled in any of the following:
    • STAT334 - Probability Models for Business and Accounting (0.50)

Leads to

Fall 2026 sections

Enrolment from UW Open Data, which can trail Quest by up to two days. Instructors and rooms: Schedule of Classes.
SectionClassEnrolledMeets
LEC 001612579 / 150TTh 11:30–12:50
LEC 002621271 / 150TTh 14:30–15:50
TUT 101611586 / 150F 10:30–11:20
TUT 102792064 / 150F 09:30–10:20

Winter 2027 sections

Enrolment from UW Open Data, which can trail Quest by up to two days. Instructors and rooms: Schedule of Classes.
SectionClassEnrolledMeets
LEC 00155880 / 125TTh 08:30–09:50
LEC 00258190 / 125TTh 14:30–15:50
LEC 7012220125 / 9999Online or by arrangement
TUT 10156840 / 250F 08:30–09:20

Resources

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Reviewed on UW Flow

58% liked it44% easy67% useful

From 198 ratings and 61 comments on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.

  • No idea what is going on ever since the second midterm.

    Nov 2023 · didn’t like it · 7 found this helpfulOn UW FlowRemove this

  • Could've been a fun and doable course as the course material is based on stat 230 mostly, but the prof is so bad. He wouldn't post his notes on learn, did not even give out assignments, only 2 midterms and final. His markings are brutal, he will take off so much marks on small things and most importantly I have heard some student in this term crying after going to his office hour because of his shitty attitude towards students who are willing to learn. Genuinely the worst prof I had as he literally makes things harder to learn. Should resign his position honestly.

    Nov 2023 · didn’t like it · 4 found this helpfulOn UW FlowRemove this

  • Easy course if you are capable of understanding all the questions in course notes. Prof Tian's Final is very fair as long as you spend sufficient time in reviewing his lecture notes and assignments. Would recommend attending his class and tutorials as best as you can! He is amazing and so much of kindness!

    Aug 2024 · liked it · 3 found this helpfulOn UW FlowRemove this

  • I still don't understand why the professor had to rush through the last three chapters in the final four weeks—especially considering there were only five chapters in total, and the last three were comparatively more difficult than the first two. Additionally, no class notes have been provided, and the professor does not use course notes. The only way to study is to take photos of his notes during class.
    Detailed solutions for the tutorials are also not provided, so you need to go to the tutorials yourself. However, the TA for the second half of the course frequently made mistakes, relying on corrections from the students. There was only one (difficult) assignment for the entire semester,…

    Dec 2023 · didn’t like it · 3 found this helpfulOn UW FlowRemove this

  • The course is probably useful and interesting if Peijun Sang had made it possible to learn any of the material.

    Nov 2023 · didn’t like it · 3 found this helpfulOn UW FlowRemove this

Discussed on r/uwaterloo

705 posts and comments in 522 threads mention STAT 330, April 2012 to December 2024. Quoted word for word, newest first; each reply sits under the post and the comment that started its branch. Search r/uwaterloo for newer posts.

Fall 2024

Stat 330 Final Bonus Question 1 point, 2 comments

u/Fold_Informal: “I saw the piazza post about a bonus question only people who attended lecture know about. Apparently the more people who know, the more marks it will give. Unfortunately I was unable to attend that lecture. Does someone know what the question will be?”

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Check it elsewhere for Fall 2026

Calendar versions

Undergraduate Calendar