Math 180A, Lecture C00

Introduction to Probability

Fall 2022: MWF 4:00-4:50 PM, CENTR 105

Announcements
Calendar
Syllabus
Piazza
Gradescope
Homeworks

Announcements

December 10:
- Solutions to the final version A / version B / version C / version D. The correct answers are marked by an asterisk.
- Updated letter grade scale
  
  A+ A A- B+ B B- C+ C C-
  
  97 91 85 81 74 68 61 56 44
December 3:
- The seats for the final exam have been randomly assigned. In order to find out your seat, go to this web page and enter your student ID. Please take it seriously: sitting in the wrong seat will be considered an academic integrity violation and will be reported to the AI Office.
December 1:
- Practice final is available for download practice final solutions.
- There will be extra office hours on Monday, December 5, 3 - 4:30 PM, AP&M 6321.
November 29:
- You can submit the CAPE reviews for this course using the link. If the overall response rate for the lecture reaches 65% your second lowest homework score will be dropped when computing the final grade (in addition to the lowest homework score)
- About the final exam:
  - The final exam will take place in person on Tuesday, December 6, 3 - 6 PM, CENTR 105;
  - You are allowed to bring two standard (A4 or 8.5x11) sheets with handwritten notes on both sides; no other notes or books are allowed; no use of electronic devices of any kind (phones, smart watches, tablets, calculators) is allowed;
  - The seats will be randomly assigned; you will receive a link to the website where you will find your assigned seats; please let me know no later than Friday if you prefer a left-handed seat;
  - You have to wear a face mask and you must have your student ID with you at all time during the exam; you must bring your own pen and/or pencil;
  - The exam will consist of approximately 16 multiple choice questions; each question will have only one correct answer; you will have to fill in a bubble sheet with your answers, so it might be a good idea to bring a pencil;
  - The final exam is cumulative and covers all the topics discussed in the lectures;
  - The exam will have multiple versions that will be assigned according to your (assigned) seats;
  - Before the start of the exam, do not enter the room until instructed by the proctors;
  - During the exam, do not remove any pages from the exam.
November 24: Homework 7 is now available for download (see below). Due: Friday, December 2, 11:59 PM.
November 18: Solutions to Midterm 2 can be downloaded here.
November 15:
- Solutions to Practice midterm 2 are available for download pdf.
- Midterm 2 problems can be downloaded here.
- Homework 6 is now available for download (see below). Due: Wednesday, November 23, 11:59 PM.
November 14: Important midterm 2 updates.
- Midterm 2 will be a take-home exam. The problems will be posted on this website on Wednesday, November 16.
- Midterm 2 will not be graded and you do not have to turn your exams in. The solutions will be posted on this website on Thursday, November 17.
- All students automatically get full score for Midterm 2. The grading schemes remain unchanged.
- Instead of the in-person midterm there will be a normal in-person lecture on November 16.
November 11: Practice midterm 2 is available for download pdf. Solutions will be presented during the lecture on Monday, November 14, and later posted on this website.
November 6: Important: There will be no in-person lecture on Monday, November 7. You can watch the prerecorded lecture here. On Wednesday, November 9, the lecture will be held in person as usually.
November 4: Homework 5 is now available for download (see below). Due Friday, November 11, 11:59 PM.
October 28: Homework 4 is now available for download (see below). Due Friday, November 4, 11:59 PM.
October 26: Solutions to Midterm 1 can be downloaded here.
October 21:
- Midterm 1 has been graded. You can submit regrade requests on Gradescope until Sunday, October 30.
- The submission deadline for Homework 3 has been changed to Wednesday, October 26, 11:59 PM.
October 17: Solutions to Practice midterm 1 are available for download pdf.
October 13:
- The office hour schedule has been updated (again). Check the timetable and the calendar.
- Homework 3 is now available for download (see below). Due Friday, October 21, 11:59 PM.
- Homework 1 has been graded. Regrades are available on Gradescope until Sunday, October 16.
- Practice midterm 1 is available for download pdf. Solutions will be presented during the lecture on Monday, October 17, and later posted on this website.
- Midterm 1 will take place (in person) on Wednesday, October 19, 4 - 4:50 PM at CENTR 105 (during the lecture).
  - the seats have been randomly assigned to the students registered for this course. In order to find out your seat, go to this web page and enter your student ID. Please take it seriously, if you are caught sitting at the wrong seat, you will lose the opportunity to drop one of the homeworks when computing your final grade;
  - you are allowed to bring one standard (A4 or 8.5x11) sheet with handwritten notes on both sides; no other notes or books are allowed; no use of electronic devices of any kind (phones, smart watches, tablets, calculators) is allowed;
  - write all your solutions on the exam paper; do not remove pages from the exam.
October 5: The office hour schedule has been updated (starting week 3). Check the timetable and the calendar.
October 3:
- Homework 2 is now available for download (see below). Due Wednesday, October 12, 11:59 PM.
- Important. If you have not done this yet, go to Canvas Quizzes and fill in the survey called First Day Survey: Tell Me About Yourself #FinAid. You have to submit this survey before the end of week 2. Submitting this survey will automatically report your commencement of academic activity in this course (required by the Department of Education). Failing to submit by the due date may lead to loss of financial aid award. You have to submit this survey independently of whether or not you have already submitted a similar survey for another class.
September 25: Homework 1 is now available for download (see below). Due Tuesday, October 4, 11:59 PM.
September 19: Homework 0 is now available for download (see below). Due Wednesday, September 28, 11:59 PM.
September 19: Welcome to MATH 180A: Introduction to Probability!

Course Information

Textbook: The required textbook for this course is

Introduction to Probability, by David F. Anderson, Timo Seppäläinen, and Benedek Valkó; DOI 10.1017/9781108235310
Reading and homework assignments will refer to this textbook as ASV.

Coursework: There will be
- homework assignments due roughly every week, typically on Fridays (starting in Week 1); they are posted below;
- two midterm exams on Weeks 4 and 8;
- and a final exam.

Piazza is an online discussion forum. It will allow you to post messages (openly or anonymously) and answer posts made by your fellow students, about course content, homework, exams, etc. The instructors and TAs will also monitor and post to Piazza regularly.
- For all questions related to the course, ask your questions on Piazza before contacting the instructor/TAs directly.
- You can sign up here.
- Note: Piazza has an opt-in "Piazza Careers" section which, if you give permission, will share statistics about your Piazza use with potential future employers. It also has a "social network" component, based on other students who've shared a Piazza-based class with you, that comes with the usual warnings about privacy concerns. Piazza is fully FERPA compliant, and is an allowed resource at UCSD. Nevertheless, you are not required to use Piazza if you do not wish.

Gradescope is an online tool for uploading and grading assignments and exams (it is now under the umbrella of Turnitin). You will turn in your homework through Gradescope, and you will access your graded exams there as well.
- Access the class Gradescope site here.
- Homework 0 below will guide you through the Gradescope sign up process for this class.

Canvas is a learning management system (LMS) used by UCSD. We will use Canvas for Quizzes and for sharing certain course materials. Make sure that you have acces to the MATH 180A C00 course.

Instructional Staff and Office Hours

Name	Role	Office	E-mail	Office hours
Yuriy Nemish	Instructor	AP&M 6321	ynemish@ucsd.edu	Wednesday 5-7 PM (AP&M 1260)
Sheng Qiao	Teaching Assistant	HSS 5056	sqiao@ucsd.edu	Wednesday 10:30 - 12 PM Thursday 10:30 - 12 PM Friday 6 - 7 PM (remotely via zoom)
Kejin Wu	Teaching Assistant	HSS 5053	kwu@ucsd.edu	Thursday 3 - 5 PM
Toni Gui	Teaching Assistant	HSS 4086A	ttgui@ucsd.edu	Thursday 1 - 2 PM Thursday 2 - 3 PM (remotely via zoom)

Please, check the following calendar for possible reschedulings of the office hours. You are welcome to attend the office hours of either of the TAs, not just your own.

Calendar

Class Meetings

	Date	Time	Room
Lecture (YN)	Monday, Wednesday, Friday	4 - 4:50 PM	CENTR 105
Discussion C01 (SQ)	Tuesday	5 - 5:50 PM	AP&M 2301
Discussion C02 (SQ)	Tuesday	6 - 6:50 PM	AP&M 6402
Discussion C03 (KW)	Tuesday	7 - 7:50 PM	AP&M 6402
Discussion C04 (TG)	Tuesday	8 - 8:50 PM	AP&M 2301

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Important dates

	Week	Date	Time	Room	Policy
Midterm Exam 1	4	Wednesday, Oct 19	4 - 4:50 PM	CENTR 105	Midterm Exams
Midterm Exam 2	8	Wednesday, Nov 16	4 - 4:50 PM	CENTR 105	Midterm Exams
Final Exam	Finals	Tuesday, Dec 6	3 - 6 PM	TBA	Final Exam

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Syllabus

Welcome to Math 180A: a one quarter course introduction to probability theory. This course is the prerequisite for the subsequent courses Math 180B/C (Introduction to Stochastic Processes) and Math 181A/B (Introduction to Mathematical Statistics), as well as for MATH 114 (Introduction to Computational Stochastics), MATH 194 (The Mathematics of Finance) and Math 189 (Exploratory Data Analysis and Inference). According to the UC San Diego Course Catalog, the topics covered are probability spaces, random variables, independence, conditional probability, discrete and continuous probability distributions, joint distributions, variance and moments, the Laws of Large Numbers, and the Central Limit Theorem.

Here is a more detailed listing of course topics, in the sequence they will be covered, together with the relevant section(s) of the textboox. While each topic corresponds to approximately one lecture, there will be some give and take here. This is a rough schedule that will be updated during the term.

Date	Week	Topic	ASV	Preliminary slides	Final slides
9/23	0	Administrivia. Definition of Probability	1.1	Slides 1	Slides 1
9/26	1	Random sampling	1.2	Slides 2	Slides 2
9/28	1	Basic Properties of Probability	1.3-1.4	Slides 3	Slides 3
9/30	1	Conditional Probability	2.1	Slides 4	Slides 4
10/3	2	Conditional probability	2.1	Slides 5	Slides 5
10/5	2	Bayes' rule	2.2	Slides 6	Slides 6
10/7	2	Independence	2.3	Slides 7	Slides 7
10/10	3	Random variables	3.1	Slides 8	Slides 8
10/12	3	Probability Distributions. CDF and PDF	3.1	Slides 9	Slides 9
10/14	3	CDF and PDF	3.2, 2.4	Slides 10	Slides 10
10/17	4	CDF and PDF. Review		Slides 11	Slides 11
10/19	4	Midterm 1
10/21	4	Independent Trials. Binomial, Geometric, and Poisson Distributions	2.4-2.5, 4.4	Slides 12	Slides 12
10/24	5	Poisson distribution. Expected Value	3.3	Slides 13	Slides 13
10/26	5	Expectation	3.3-3.4	Slides 14	Slides 14
10/28	5	Variance. Normal (Gaussian) Distribution	3.4-3.5	Slides 15	Slides 15
10/31	6	Normal (Gaussian) Distribution	3.5	Slides 16	Slides 16
11/2	6	Normal Approximation. Law of Large Numbers	4.1	Slides 17	Slides 17
11/4	6	Confidence intervals	4.3	Slides 18	Slides 18
11/7	7	Confidence intervals. Poisson approximation	4.4	Slides 19	Slides 19	Prerecorded video
11/9	7	Exponential Distribution	4.5	Slides 20	Slides 20
11/11	7	Veterans Day
11/14	8	Moment generating function	5.1	Slides 21	Slides 21
11/16	8	Moment generating function	5.1	Slides 22	Slides 22
11/18	8	Joint distribution. Independence	6.1-6.3	Slides 23	Slides 23
11/21	9	Joint distribution. Independence	6.1-6.3	Slides 24	Slides 24
11/23	9	Expectations of sums and products	8.1-8.3	Slides 25	Slides 25
11/25	9	Thanksgiving
11/28	10	Covariance, correlation, and variance of sums	8.4	Slides 26	Slides 26
11/30	10	Correlation. Tail probabilities	9.1	Slides 27	Slides 27
12/2	10	Law of Large Numbers. Central Limit Theorem	9.2-9.3	Slides 28	Slides 28

Prerequisite: The only prerequisites are calculus up to and including Math 20C (Multivariate Calculus) or MATH 31BH (Honors Multivariable Calculus). Math 109 (Mathematical Reasoning) is also strongly recommended as a prerequisite or corequisite.

Lecture: You are responsible for material presented in the lecture whether or not it is discussed in the textbook. You should expect questions on the exams that will test your understanding of concepts discussed in the lecture.

Homework: Homework assignments are posted below, and will be due at 11:59 PM on the indicated due date. You must turn in your homework through Gradescope; if you have produced it on paper, you can scan it or simply take clear photos of it to upload. Your lowest homework score will be dropped. It is allowed and even encouraged to discuss homework problems with your classmates and your instructor and TA, but your final write up of your homework solutions must be your own work.

Exams

Midterm Exams: The two midterm exams will take place during the lecture time on the dates listed above.

You may bring one 8.5 by 11 inch sheet of paper with handwritten notes (on both sides) with you to each midterm exam; no other notes (or books) will be allowed.
No calculators, phones, or other electronic devices will be allowed during the midterm exams.
There will be no makeup midterm exams.
The detailed midterm exam instructions will be posted one week before each midterm.

Final Exam: The final examination will be held at the date and time stated above.

It is your responsibility to ensure that you do not have a schedule conflict involving the final examination; you should not enroll in this class if you cannot take the final examination at its scheduled time.
You may bring two 8.5 by 11 inch sheets of paper with handwritten notes (on both sides) with you; no other notes (or books) will be allowed.
No calculators, phones, or other electronic devices will be allowed during the final examination.
There will be no makeup final exam.
The detailed final exam instructions will be posted one week before the final exam.

The above exam policies will be applied to in-person exams. The exam policies will be changed in case of the change in exam modality. More detailed instructions will be posted on this website later.

Administrative Links: Here are two links regarding UC San Diego policies on exams:

Exam Responsibilities An outline of the responsibilities of faculty and students with regard to final exams

Policies on Examinations The Academic Senate policy regarding final examinations (These are the rules!)

Regrade Policy:

Your exams and homeworks will be graded using Gradescope. You will be able to request regrades directly from your TA through Gradescope for a specified window of time. Be sure to make your request within the specified window of time; no regrade requests will be accepted after the deadline. Note: Your grader will consider your regrade request only if you have explained clearly, thoroughly, and politely why you think an error in grading was made.

Grading: Your cumulative average will be computed as the best of the following weighted averages:

20% Homework, 20% Midterm 1, 20% Midterm 2, 40% Final Exam
20% Homework, 20% Best midterm, 60% Final Exam

Your course grade will be determined by your cumulative average at the end of the quarter, and will be based on the following scale:

A+	A	A-	B+	B	B-	C+	C	C-
97	93	90	87	83	80	77	73	70

The above scale is guaranteed: for example, if your cumulative average is 80, your final grade will be at least B-. However, your instructor may adjust the above scale to be more generous.

Academic Integrity: UC San Diego's code of academic integrity outlines the expected academic honesty of all studentd and faculty, and details the consequences for academic dishonesty. The main issues are cheating and plagiarism, of course, for which we have a zero-tolerance policy. (Penalties for these offenses always include assignment of a failing grade in the course, and usually involve an administrative penalty, such as suspension or expulsion, as well.) However, academic integrity also includes things like giving credit where credit is due (listing your collaborators on homework assignments, noting books or papers containing information you used in solutions, etc.), and treating your peers respectfully in class. In addition, here are a few of our expectations for etiquette in and out of class.

Entering/exiting class: Please arrive on time and stay for the entire class/section period. If, despite your best efforts, you arrive late, please enter quietly through the rear door and take a seat near where you entered. Similarly, in the rare event that you must leave early (e.g. for a medical appointment), please sit close to the rear exit and leave as unobtrusively as possible.
Noise and common courtesy: When class/section begins, please stop your conversations. Wait until class/section is over before putting your materials away in your backpack, standing up, or talking to friends. Do not disturb others by engaging in disruptive behavior. Disruption interferes with the learning environment and impairs the ability of others to focus, participate, and engage.
Electronic devices: Please do not use devices (such as cell phones, laptops, tablets, iPods) for non-class-related matters while in class/section. No visual or audio recording of the class meetings is allowed without prior permission of the instructor (whether by camera, cell phone, or other means).
E-mail etiquette: You are expected to write as you would in any professional correspondence. E-mail communication should be courteous and respectful in manner and tone. Please do not send e-mails that are curt or demanding.

Accommodations:

Students requesting accommodations for this course due to a disability must provide a current Authorization for Accommodation (AFA) letter issued by the Office for Students with Disabilities (OSD) which is located in University Center 202 behind Center Hall. The AFA letter may be issued by the OSD electronically or in hard-copy; in either case, please make arrangements to discuss your accommodations with me in advance (by the end of Week 2, if possible). We will make every effort to arrange for whatever accommodations are stipulated by the OSD. For more information, see here.

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Homework

Weekly homework assignments are posted here. Homework is due by 11:59 PM on the posted date, through Gradescope. Late homework will not be accepted.

Homework 0, due Wednesday, September 28.

Homework 1, due Tuesday, October 4.

Homework 2, due Wednesday, October 12.

Homework 3, due Wednesday, October 26.

Homework 4, due Friday, November 4.

Homework 5, due Friday, November 11.

Homework 6, due Wednesday, November 23.

Homework 7, due Friday, December 2.