Inequalities and Asymptotics
Week 04, Spring 2022
- Start: Monday, February 7
- End: Friday, February 11
Summary
This will be our last week reviewing probability concepts. First we’ll look at some useful inequalities. Then we will discuss asymptotics, leading to the central limit theorem.
Learning Objectives
After completing this week, you are expected to be able to:
- Provide bounds on probabilities using well known inequalities.
- Understand the difference between convergence in probability and distribution.
- Understand the central limit theorem.
- Approximate probabilities based on asymptotic normality.
- Understand the weak law of large numbers.
- Use the delta method.
Reading
| Source | Section |
|---|---|
| Wasserman | 4.1 - 4.4 |
| Wasserman | 5.1 - 5.7 |
| Evans and Rosenthal | 3.6 |
| Evans and Rosenthal | 4.1 - 4.6 |
| Marden | 8.1 - 8.7 |
| Marden | 9.1 - 9.5 |
Video
| Title and Slides | Link | Mirror |
|---|---|---|
| 4.0 - Welcome to Week 04 | 4.0 - YouTube | 4.0 - ClassTranscribe |
| 4.1 - Inequalities | 4.1 - YouTube | 4.1 - ClassTranscribe |
| 4.2 - Convergence | 4.2 - YouTube | 4.2 - ClassTranscribe |
| 4.3 - Central Limit Theorem Proof | 4.3 - YouTube | 4.3 - ClassTranscribe |
Assignments
- Homework 03
- Source:
RMarkdown - Due: Monday, February 14
- Submission: Gradescope
- Solution: Canvas
- Source:
Office Hours
| Staff and Link | Day | Time |
|---|---|---|
| Zoom with David | Monday | 5:30 PM - 6:30 PM |
| Zoom with Eugene | Monday | 9:00 PM - 10:00 PM |
| Zoom with Eugene | Thursday | 12:00 PM - 1:00 PM |
| Zoom with David | Thursday | 5:00 PM - 7:00 PM |
| Discussion Forum | Any! | Any! |