University of California, Irvine

Department of Mathematics


Math 130B: Probability II
Winter 2021 - Remote Syllabus


Course Description & Materials

Joint distributions, sums of independent random variables, conditional distributions and conditional expectation, covariances, moment generating functions, limit theorems.

Prerequisites: Math 130A

Textbook: S. Ross, First Course in Probability, 9th edition. ISBN: 9780321794772*

* Please make sure to have the correct version of the textbook as homework problems will be assigned from this version. If you have a different version, please make sure to double check all problems before submitting your assignment.


Remarks on Remote Learning:

My goal is to give you the best quality education I can given the circumstances. While this predicament and situation is not an excuse to lower our standards and expectations, we must remain cognizant and open-minded to the various personal and intellectual challenges we face in the upcoming quarter. With that in mind, this course has been redesigned to accommodate everyone as best as possible while preserving the the quality of instruction. Below are some important remarks regarding remote learning and this class.

1. Communication: Throughout the quarter, especially in this remote setting, communication is key. Let me know as soon as possible when issues regarding technology, restricted access to content, or other situations arise that may negatively impact your ability to learn the material. The earlier you communicate, the more that can be done to accommodate you and/or your classmates. In addition, if you have any feedback on the structure, lectures, or notes at any time throughout the quarter, please feel free to send me your constructive critiques. This will be my first quarter teaching live online and I welcome any suggestions that can improve your learning experience.

2. Learning: It will not be enough to sit through and watch just the pre-recorded videos. Have you ever watched someone teach a skill, for example how to juggle, and immediately master that skill on your first try?1 Mathematics is the same way. You cannot master the material from watching me solve problems. I highly encourage you to not just watch the videos but also take notes, as if you were in a traditional learning environment, and pause the video to answer out loud questions that I pose. Working out practice problems from the homework assignments and your textbook will also be crucial to deepening your understanding of the material as well as your success in the course.

3. Participation: A difficult component of remote learning is fostering a sense of community and togetherness. In an effort to cultivate and encourage communication amongst the class, I have decided to incorporate a participation component to the course. See below for details.

4. Zoom: Whenever possible, I invite you to share your video during office hours and other meetings. It’s welcoming to see your smiling faces, especially during remote OH. If you prefer not to have a webcam on, I encourage you to change your default picture on Zoom to one of yourself.

Finally, let me end by saying that if you are struggling this quarter for any reason, please let me know — I may not be able to help in all situations, but I am happy to talk and to try to direct you to someone who can help. Thanks for reading and I look forward to meeting you this quarter!


Tentative Lesson Plan (updated throughout the quarter)


Course Structure

Lectures: Lectures will be held online at 11am PST via Zoom. The lectures and accompanying notes will be posted online later the same evening for students who cannot attend lecture. Lecture videos will be broken up into 5-10 minute clips that encapsulate main content and/or collections of examples for you to try on your own.

Homework: Homework will be posted every Wednesday and due the following Friday via gradescope. Problems will be a mixture of past exam problems and problems assigned from the textbook. The lowest homework grade will be dropped. You are welcome and encouraged to form study groups and discuss homework with other students, but you must write your solutions individually. Assignments will be submitted via gradescope in 1 pdf file. Late homework will be penalized 2 points for every day it’s late with no exceptions. Each assignment is worth 10 points. 5 points will be rewarded for completion and two randomly selected problems will be graded for accuracy for the remaining 5 points.

Quizzes: Organized by TA. Details to come.

Exams: This course will consist of 2 exams — 1 midterm and 1 cumulative final. You will have a 24 hour block to complete your exams. You may use your notes, textbook, and your own previous assignments during the exam. You may not consult other people, other peoples’ work, or use the internet.

Office Hours: Please feel free to have your video on but keep your mic on mute unless you’re speaking. There will be two types of office hours: group office hours and one on one office hours.

On Wednesdays I will host group office hours. During group office hours, anyone will be able to join the Zoom meeting at any time throughout the hour. This is a great time to ask questions about the materials, homework assignments, quizzes, and so on.

On Mondays, I will host one on one office hours. During one on one office hours, the zoom meeting will have a waiting room and students will be let into the office hour one at a time. If you prefer to discuss problems privately, this is a great option.

Participation: Participation points will be awarded throughout the quarter. Your goal is to reach 60 participation points before the quarter ends. At the end of the quarter, your participation will be totaled and divided by 60 to calculate your participation grade. (For example, if you accumulate 50 participation points your score is 50/60.) You may not be awarded more than 60 points. There are plenty of ways to earn participation credit throughout the quarter! The activities are summarized in the table below and guidelines are provided here.

- Introductions: To receive points for posting an introduction on piazza, you must write at least 5 sentences about yourself. In order to receive points for responding to a student’s introduction, you must meaningfully engage with their introduction. For example, simply responding “Hello! It’s nice to meet you.” will not award you any points. An acceptable response would be, “It’s nice to meet you! I also am attending from the east coast time zone. Do you want to get together for a study session some time?”.

- Office hours: When receiving points for attending an office hour, you must ask the TA or myself to record your attendance (this can be done in audio or via chat), stay for at least 10 minutes, and ask at least one material-related question.

- Piazza Questions: To get points for posting a question on piazza, you must meaningfully engage with the course material. For example, “When is Midterm 1?” can be posted on the piazza forum but will not be awarded participation points. An example of a credited post would be, “How do you show the linearity of expected value for continuous random variables?” When responding to a question, try your best to refrain from giving away homework answers directly and instead provide guidance and intuition. Questions are not restricted to a single answer by a single student. If you have additional hints and guidance to add, please feel free add your response.


Grading

Academic honesty will be strictly enforced. Any and all violations to the UCI Academic Integrity Policy will be immediately reported and handled through the Office of Academic Integrity and Student Conduct (OAISC).

Your numerical grade will be based on homework assignments, participation, quizzes, midterms, and final exams. To accommodate the exceptional circumstances presented in Winter 2021, there will be two rubrics for calculating your final percentage grade and you will receive the better of the two.

Rubric:

Participation - 10%
Homework - 15%
Quizzes - 15%
Midterm - 25%
Final Exam - 35%


Final Grade: At the end of the quarter your final numerical score (computed on a scale of 0-100 as an average of the different grade components as described above) will be translated into a final letter grade according to a curve whose precise nature I will decide upon at that time to ensure a reasonable grade distribution. However, you can be assured that a final numerical score of:

- 90 or higher & guarantees an A- or better letter grade
- 80 or higher & guarantees a B- or better letter grade
- 70 or higher & guarantees a C- or better letter grade
- 60 or higher & guarantees a D- or better letter grade

Please keep in mind that, regardless of whether you’re in a traditional learning environment or a remote one, a letter grade is simply a quantitative indication of the level of understanding of the course material throughout the quarter. I want to emphasize that your grade in this course is simply a measure of how deeply and how well you learned the material covered, and not a measure of personal worth or overall intellect. Please feel free to speak with me at any time if you have any questions or concerns.


Waitlist

If you are currently on the waitlist, please keep up with the material as if you were taking the class offiffifficially. Also, neither I nor the TA have the ability to add you from the waitlist. Please contact [email protected] regarding your status and for questions and concerns.


Additional Resources

- Suggested Syllabus for Math 130A: http://www.math.uci.edu/sites/math.uci.edu/ files/130A%20syllabus%20.doc
- UCI Academic Integrity: https://aisc.uci.edu/policies/academic-integrity/index.php
- COVID-19 UCI Student Resources: https://uci.edu/coronavirus/students/index.php
- Aforementioned Hidden Brain Episode: https://www.npr.org/2019/02/05/691697963/close-enough-the-lure-of-living-through-others