PSTAT 120B: Mathematical Statistics, I

Lectures and Course Schedule

Instructor
Quarter

Ethan Marzban

Summer Session A, 2024

Lecture Slide Decks

  • Topic 0: An Introduction to the Course

  • Topic 1: Conditional Distributions and Expectations [Updated 6/26/24]

  • Topic 2: Transformations

  • Topic 3: Estimation

    • Part 1 (these slides will be updated periodically, so please check back regularly!) [Last updated: 7/10/24]

    • Part 2 (more work will be done on the whiteboard) [Last updated: 7/11/24]

    • Part 3 [Last updated: 7/15/24]

    • Part 4 [Last updated: 7/18/24]

    • Part 5 [Last updated: 7/22/24]

  • Topic 4: Sufficiency and MVUEs [Updated 7/24/24]

  • Topic 5: Confidence Intervals

    • Part 1 [Last updated: 7/31/24] Typos have been fixed

    • Part 2 [Last updated: 7/25/24]

  • Topic 6: Hypothesis Testing

    • Part 1 [Last updated: 7/31/24] ; Typo has been fixed, and a few slides have been added based on our discussion in Lecture.

      • PLEASE NOTE: I made a bit of an error in the final example previously. In a two-sided \(T-\)test, the test statistic is \(\left| \frac{\overline{Y}_n - \mu_0}{s_n / \sqrt{n}} \right|\) INCLUDING THE ABSOLUTE VALUES. (Some conventions do not include the absolute values in the term “test statistic,” but we will adopt the convention that “test statistic,” in the two-sided case, includes the absolute values. So please be aware of this for the final exam!)

    • Part 2 [Last updated: 7/31/24]


Homework Assignments

  • HW01: Due by 11:59pm on Wednesday, June 26, 2024 on Gradescope


  • HW02: Due by 11:59pm on Tuesday, July 2, 2024 on Gradescope


  • HW03: Due by 11:59pm on Wednesday, July 10, 2024 on Gradescope
    • Solutions can be found at this link, and


  • HW04: Due by 11:59pm on Monday, July 15, 2024 on Gradescope


  • HW05: Due by 11:59pm on Wednesday, July 24, 2024 on Gradescope
    • Solutions can be found at this link, and


  • HW06: Due by 11:59pm on Tuesday, July 30, 2024 on Gradescope. Will be graded only on completion - the bulk of the problems have been worked through (or will be worked through) in Lecture.

Quiz Information

  • Quiz03:
    • Topics Covered: Homework 5 concepts (e.g. Method of Moments, Maximum Likelihood [including equivariance], Sufficiency)
    • Formula Sheet:
    • Solutions:


  • Quiz02:
    • Topics Covered: All of Topic 2.5 (Bivariate and Multivariate Transformations)
    • Formula Sheet:
    • Solutions:


  • Quiz01:
    • Topics Covered: All of Topic 01 (including conditional expectations; just know it at the level of the coin-and-die example)
    • Coverpage and Formula Sheet:
    • Solutions:
    Please note: there were several versions of the quiz that differed only slightly (in numbers and problem contexts). I will typically only be posting solutions to one version, again because the different versions were very similar to one another. You’re welcome to bring questions about your specific quiz to Office Hours (either the Instructor’s or the TAs’)!

Course Schedule

Note

This page will be updated as we progress through the quarter; please check back regularly for updates!

Emoji Meanings
  • 🧑‍🏫 = Lecture
  • 📖 = Textbook Reading
  • 📄 = Discussion Section Worksheet

Last Updated: 7/3/24

WEEK DATE TEXTBOOK SECTIONS TOPIC CORRESPONDING SLIDE DECK SECTION MATERIALS THINGS DUE

1

 Mon, Jun 24

📖 Sections 5.3 - 5.4

🧑‍🏫 Lec01: Conditional Distributions

1: Conditional Distributions / Expectations

Tue, Jun 25

📖 Sections 5.3 - 5.4

🧑‍🏫 Lec02: Conditional Expectations

1: Conditional Distributions / Expectations

Wed, Jun 26

📖 Section 5.11

🧑‍🏫 Lec03: Transformations

1: Cond. Dist / Expec
2: Transformations

HW01 Due (only Problems 1 - 3 need to be submitted; please see Canvas Announcement)


 Thu, Jun 27

📖 Sections 6.1 - 6.3

🧑‍🏫 Lec04: Transformations

2: Transformations

📄 Wksht02 QUIZ 01
(in-person)

2

 Mon, Jul 1

📖 Sections 6.4 - 6.5

🧑‍🏫 Lec05: Transformations

2: Transformations

Tue, Jul 2

🧑‍🏫 Lec06: Review/Catch-Up

HW02 Due


 Wed, Jul 3

🧑‍🏫 MIDTERM 1


Thu, Jul 4

HOLIDAY: No Lecture or Sections

3

 Mon, Jul 8

📖 Sections 6.2, 6.7

🧑‍🏫 Lec07: Bivariate Transformations

2.5: Multivariate Transformations

Tue, Jul 9

📖 Sections 7.1 - 7.2

🧑‍🏫 Lec8: Multivariate Transformations / Sampling Distributions

2.5: Multivariate Transformations

Wed, Jul 10

📖 Sections 8.1 - 8.2

🧑‍🏫 Lec9: Small-Sample Estimation

3: Estimation

HW03 Due


 Thu, Jul 11

📖 Sections 8.2, 9.3

🧑‍🏫 Lec10: Large-Sample Estimation

3: Estimation

📄 Wksht04
📄 Wksht04 Solns
QUIZ 02
(in-person)

4

 Mon, Jul 15

📖 Sections 9.3, 7.3

🧑‍🏫 Lec11: Consistency; CLT

3: Estimation

Tue, Jul 16

🧑‍🏫 Lec12: Review/Catch-Up

HW04 Due


 Wed, Jul 17

🧑‍🏫 MIDTERM 2


Thu, Jul 18

📖 Section 9.6

🧑‍🏫 Lec13: Method of Moments

3: Estimation

5

 Mon, Jul 22

📖 Section 9.7

🧑‍🏫 Lec14: Maximum Likelihood Estimation

3: Estimation

Tue, Jul 23

📖 Section 9.4, 9.5

🧑‍🏫 Lec15: Sufficiency / MVUE

4: Sufficiency

Wed, Jul 24

📖 Sections 8.5 - 8.6, 8.8 - 8.9

🧑‍🏫 Lec16: Confidence Intervals

5: Confidence Intervals

HW05 Due


 Thu, Jul 25

📖 Sections 10.1 - 10.3

🧑‍🏫 Lec17: Confidence Intervals / Hypothesis Testing

5: Confidence Intervals / 6: Hypothesis Testing

📄 Wksht07
📄 Wksht067Solns
QUIZ 03
(in-person)

6

 Mon, Jul 29

📖 Sections 10.4, 10.6 - 10.7

🧑‍🏫 Lec18: Hypothesis Testing

6: Hypothesis Testing

Tue, Jul 30

📖 Sections 10.8 - 10.9

🧑‍🏫 Lec19: Hypothesis Testing

6: Hypothesis Testing

📄 Wksht08
HW06 Due


 Wed, Jul 31

📖 Sections 10.10 - 10.11

🧑‍🏫 Lec20: Hypothesis Testing

6: Hypothesis Testing

Thu, Aug 1

🧑‍🏫 Lec21: Review for Final

📄 Wksht09

Some More Information

  • Midterm exams take place on Wednesdays (twice throughout the quarter, on the dates listed in the calendar above).
  • Homework assignments are due on Wednesdays in non-exam weeks, and on Tuesdays in exam weeks.
  • Quizzes take place synchronously and in-person, during the first 20 minutes of Thursday Discussion Sections (on the dates outlined in the calendar above).
  • I recommend reading the corresponding Textbook sections before coming to lecture.