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Math 407: Probability Theory

I am your instructor Prof Geske (guess-key) and am happy to welcome you to the course! Please explore the course webpage.

Announcements

Welcome!

Welcome! This is your Math 407 instructor Prof Geske! I would like you to kindly do the following prior to your first lecture.

  • Access the course webpage and read through it. Almost all of the course content, including the syllabus, is found at this webpage. I will not discuss the syllabus in great detail during lecture, but will be happy to answer questions about it, so do read thorough it first.
  • Verify that you do not have any conflicts with the assigned exam dates. Email me immediately if you do!
  • Only if you require testing accomodations: initiate your registration with OSAS.
  • Access the Lecture 1 handout in the Daily Schedule on the course webpage. I will print a copy for you for the first lecture, however you may also prepare it on your own notetaking device.
  • Access Brightspace and find our course page. Click the Gradescope tab and sign up. Gradescope is how you will submit your homework for grading. Besides this instance, we will use Brightspace very rarely.
  • You should also have received an announcement on Brightspace detailing the Course ID and Course Key for our MyOpenMath course. Please sign up.

sent: Fri Jan 9

Old Announcements

Office Hours

Instructor Email Office Hours Location
Prof Geske geske (at) usc (dot) edu KAP 244A
Alex Fu alexfu (dot) math (at) usc (dot) edu Math Center (KAP 263)
Alex Clay ajclay (at) usc (dot) edu Math Center (KAP 263)

You are encouraged to attend the office hours of any instructor. To gain the greatest advantage from office hours I recommend preparing your questions in advance. If it is impossible for you to attend these office hours but would still like to meet: feel free to reach out to your instructor or TA to schedule an alternative time to meet.

Time Start Time End Mon Tue Wed Thu Fri
9AM 10AM
10AM 11AM
11AM 12PM
12PM 1PM
1PM 2PM
2PM 3PM
3PM 4PM
4PM 5PM Geske
5PM 6PM Geske
6PM 7PM Geske

Daily Schedule

In this table you will find posted a pdf scaffold posted before each lecture, which we will fill in during class. You will also find posted, after each exam, solutions to that exam.

Monday Tuesday Wednesday Thursday Friday
Jan 12

Lecture 01 (A1)
Jan 13 Jan 14

Lecture 02 (A1)
Jan 15 Jan 16

Lecture 03 (A1)
Jan 19

No Class
Jan 20 Jan 21

Lecture 04 (A2)
Jan 22 Jan 23

Lecture 05 (A2)
Homework 1
Jan 26

Lecture 06 (A3)
Jan 27 Jan 28

Lecture 07 (A3)
Jan 29 Jan 30

Lecture 08 (A3)
Homework 2
Feb 02

Lecture 09 (A4)
Feb 03 Feb 04

Lecture 10 (A4)
Feb 05 Feb 06

Lecture 11 (A5)
Homework 3
Feb 09

Lecture 12 (A5)
Feb 10 Feb 11

Lecture 13 (A5)
Feb 12 Feb 13

Lecture 14 (B1)
Homework 4
Feb 16

No Class
Feb 17 Feb 18

Midterm A
Feb 19 Feb 20

Lecture 15 (B1)
Feb 23

Lecture 16 (B1)
Feb 24 Feb 25

Lecture 17 (B2)
Feb 26 Feb 27

Lecture 18 (B2)
Homework 5
Mar 02

Retake A
Mar 03 Mar 04

Lecture 19 (B3)
Mar 05 Mar 06

Lecture 20 (B4)
Homework 6
Mar 09

Lecture 21 (B4)
Mar 10 Mar 11

Lecture 22 (B5)
Mar 12 Mar 13

Lecture 23 (B5)
Homework 7
Mar 16

No Class
Mar 17

No Class
Mar 18

No Class
Mar 19

No Class
Mar 20

No Class
Mar 23

Midterm B
Mar 24 Mar 25

Lecture 24 (C1)
Mar 26 Mar 27

Lecture 25 (C1)
Homework 8
Mar 30

Lecture 26 (C2)
Mar 31 Apr 01

Lecture 27 (C2)
Apr 02 Apr 03

Lecture 28 (C3)
Homework 9
Apr 06

Retake AB
Apr 07 Apr 08

Lecture 29 (C3)
Apr 09 Apr 10

Lecture 30 (C4)
Homework 10
Apr 13

Lecture 31 (C4)
Apr 14 Apr 15

Lecture 32 (C5)
Apr 16 Apr 17

Lecture 33 (C5)
Homework 11
Apr 20

Midterm C
Apr 21 Apr 22

Lecture 34 (FinalOnly)
Apr 23 Apr 24

Lecture 35 (FinalOnly)
Apr 27

Lecture 36 (FinalOnly)
Apr 28 Apr 29

Lecture 37 (FinalOnly)
Apr 30 May 01

Retake ABC
Homework 12
May 04

No Class
May 05

No Class
May 06

Final Exam
May 07

No Class
May 08

No Class

Homework Guidelines

Where do I find the homework problem list? MyOpenMath!

The problem list is found at ☞ MyOpenMath. You will have received the CourseID and Enrollment Key by email, and can also find it in the associated Gradescope assignment. On MyOpenMath you can enter answers to problems, and your answer will be automatically checked without the possibility of penalty. You will not submit your assignments for grading through MyOpenMath: please read the next section.

Where do I submit homework for grading? Gradescope!

You submit your homework for credit-based grading through ☞ Gradescope, not MyOpenMath. You should join our Gradescope course by accessing Gradescope through ☞ Brightspace. MyOpenMath is only there to provide you the problems and let you check your answers. Anything submitted through MyOpenMath will not be considered for credit.

How do I submit homework? Read on.

Scan and upload your work either as pdfs or images through Gradescope. For pdfs: you should use Gradescope to tag each page with the problems it has. ☞ Here is how. For images: you should be asked to upload an image for each problem. Ensure your submissions are properly oriented (e.g. not sideways). Any problem that has not been assigned to a page or image will receive zero credit. Any submission that is illegible will receive zero credit.

Do I need to show work? Absolutely!

You are graded on your work, not your final answers. Final answers with no or very insufficient work will receive zero credit.

Often the MyOpenMath problems will offer hints with steps for you to solve: in yellow boxes. You do not need to include solutions to the hints if you opted to solve the problem differently.

Can I collaborate? Within reason!

Collaboration is encouraged. Copying the work of others is not. If in doubt: you should be able to recreate your solution to the problem if spontaneously put on the spot. External resources are allowed, but your intention should not be to simply locate solutions.

How is homework graded?

2 problems will be randomly selected from each assignment, and those same problems will be graded out of 3 points on Gradescope for each student. Therefore each homework is out of 6 points. Regrade requests will be due about one-and-a-half weeks after the original homework due date, except for the final homework, for which regrade requests will be due a little less than a week after the homework.

What impact does homework have on my final grade?

Homework is worth 15% of your final grade. Your lowest 2 homework scores will be dropped.

Can I submit late homework?

Late homework will be accepted with a total deduction of 0.1 points (out of 6) if submitted by Sat at 2am, of 0.2 points if submitted by Sat at 5pm, of 0.5 points if submitted by the end of Saturday, of 0.7 points if submitted by Sun at 5pm, and of 1 points if submitted by the end of Sun. Homework will not be accepted after that Sunday. No exceptions are given.

Syllabus

The content of this syllabus is subject to change.

Section Time Location
39625 11-11:50am DMC 156
39992 1-1:50pm GFS 101

Course Materials

The textbook is recommended but not required.

Textbook Author Edition
First Course In Probability Sheldon Ross 10th

Course Structure

This course is broken up into Unit A, Unit B, and Unit C. Each unit consists of 5 topics. For a total of 15 topics. There is also a topic that is exclusive to the final.

Topic Name Description
A1 Counting Count combinations and permutations. Use binomial and multinomial coefficients. Use stars and bars. Apply to word problems.
A2 Axioms of Probability Use the axioms of probability. Use the inclusion exclusion principle. Apply to word problems.
A3 Conditional Probability Compute conditional probability. Assess and use independence of events. Use the multiplication rule. Use the law of total probability. Use Bayes's formula. Apply to word problems.
A4 Discrete Random Variables Compute probabilities and conditional probabilities involving discrete random variables including the following. Binomial random variable. Poisson random variable. Geometric random variable. Apply to word problems.
A5 Expectation and Variance Compute expected value and variance and covariance of discrete random variables. Use properties of expected value and variance. Apply to word problems.
B1 Continuous Random Variables Calculate probability and expectation and variance of continuous random variables.
B2 Normal Distributions Calculate probabilities and expectations and variances involving normal random variables. Approximate binomial distributions using normal random variables with a continuity correction.
B3 Exponential + Gamma + Cauchy + Beta Distributions Calculate probabilities involving exponential distributions and gamma distributions and Cauchy distributions and beta distributions. Decide when one of these distributions is most appropriate.
B4 Joint Distributions Use joint distributions and to calculate probabilites and probability density functions. Use joint distributions to decide when variables are independent.
B5 Joint + Conditional Probability Use convolutions to compute probabilities of sums of independent variables. Use conditional density functions to compute conditional probability.
C1 Joint + Jacobians Use the Jacobian to find joint density functions of functions of random variables. Calculate probability and expected values in these situations.
C2 Joint + Expectation and Covariance Use joint distributions to compute expected value and variance and covariance and correlation. Use properties of expected value and variance. Use indicators functions to compute expected value.
C3 Joint + Conditional Expectation Use joint distributions to compute conditional expectation/variance. Use properties of conditional expectation/variance.
C4 Moments Calculate moments using expected values of binomials. Find moment generating functions and use them to calculate moments.
C5 Limit Theorems Apply bounds including the Markov inequality and the Chebyshev inequality and the Chernoff bounds. Apply the weak and strong laws of large numbers. Apply the Central Limit Theorem.
Final Only Poisson Processes and Markov Chains

See the ☞ Daily Schedule for a day-by-day breakdown of our progression through the units.

Grading is broken up into Homework, Topic Mastery, and the Final Exam.

Category Weight Total Quantity of Items in Category Weight Per Item
Homework 15% [12 HWs - lowest 2 dropped] = [10 counted HWs] 1.5% per non-dropped HW
Topic Mastery 60% 15 topics 4% per topic
Final Exam 25% 1 exam 25%
Homework

Homework will be due Fridays at 11:59pm, with a few exceptions. See the ☞ Daily Schedule for details.

Homework Guidelines. Please see the ☞ Homework Guidelines tab.

Contribution to Final Grade. Homework counts for 15% of your final grade. Your lowest 2 homework grades will be dropped.

Topic Mastery

There are 15 topics (A1-A5, B1-B5, C1-C5) which were listed earlier in the syllabus.

Individual Topic Grading. Each topic is graded out of 4 points. 4 points indicates mastery. Topic grading will be assessed using Midterms and Retakes.

Date Assessment Time Location
Wed 2/18/26 Midterm A Your Lecture Time Your Lecture Classroom
Mon 3/2/26 Retake ≤A Your Lecture Time Your Lecture Classroom
Mon 3/23/26 Midterm B Your Lecture Time Your Lecture Classroom
Mon 4/6/26 Retake ≤B Your Lecture Time Your Lecture Classroom
Mon 4/20/26 Midterm C Your Lecture Time Your Lecture Classroom
Fri 5/1/26 Retake ≤C Your Lecture Time Your Lecture Classroom

Each Midterm is tied to a unit and will have a single problem (with parts) for each each topic in that unit. For example Midterm A is tied to Unit A and will have A1, A2, A3, A4, and A5 problems. Each problem will be graded out of 4 points, indicating your score on that topic.

Each Retake is tied to all units up to that point and will have a single problem (with parts) for each topic in that unit. For example Retake ≤B is tied to Unit A and Unit B and will have A1, A2, ..., A5, B1, B2, ..., B5 problems. Each problem will be graded out of 4 points, indicating your score on that topic.

Your final score on a topic will be the maximum of your scores on each assessment. For example if your scores on A3 were [A3 on Midterm A: 1 points] and [A3 on Retake ≤A: 2 points] and [A3 on Retake ≤B: 3 points] and [A3 on Retake ≤C: 2 points] then your final score on A3 would be 3 points, as this was the maximum of your scores. Note that this means, if you ever score 4 points on a topic in an assessment, then you are effectively done with that topic, at least until the final exam.

Midterm and Retake Guidelines. Calculators are not allowed on any Midterms or Retakes. Notes are not allowed on any Midterms or Retakes. You will be provided a ☞ formula sheet however.

Midterm/Retake Absences. Exams must be taken in--person on the specified day. No exceptions are given, except for Midterm C which occurs during the week of Thanksgiving, which you may opt to take on the Friday before Thanksgiving instead, still in--person.

Otherwise, if you miss a midterm/retake for a valid and documented reason (e.g. sickness with a note from your doctor), then after the final exam has been graded, you may select up to 3 topics that appear on both that midterm/retake and on the final exam and, for each, replace your missing topic score on that midterm/retake with a substitute score from the final exam. Note that certain topics may not appear on the final exam, but you will not know which until the final exam has occurred. If you miss multiple midterms/retakes, the maximum total number of substitute scores from the final exam you can use is 5.

Regrade Requests. If you believe an error has been made in grading, a regrade request can be submitted through Gradescope. Regrade requests are due about one-and-a-half weeks after each assessment, except for Retake ABC, in which case the regrades will be due a little less than one week after the assessment.

Contribution to Final Grade. Topic Mastery counts for 60% of your final grade. Therefore each topic contributes 4% to your final grade.

Final Exam

Our sections will have a unique final exam not shared by other instructors.

Date Time Location
11am Section: Wed May 6 11am-1pm usual classroom
1pm Section: Wed May 6 2-4pm usual classroom

It is university policy that no student may take this exam early or be allowed to skip it. If you miss the final exam (and were in a position to pass the course prior to taking the final exam) then your only option is to take an "Incomplete" and take the final exam next semester.

Final Exam Guidelines. Calculators are not allowed on any Midterms or Retakes. You will be provided a ☞ formula sheet for the final exam, and are not allowed other notes.

Discussion Section

Section TA Time Location
39626 Alex Fu Tu 12-12:50pm KAP 167
39627 Alex Fu Tu 1-1:50pm KAP 167
39993 Alex Clay Tu 2-2:50pm THH B10
39994 Alex Clay Tu 3-3:50pm THH B10

Attending and participating in discussion section is essential for success in the course.

In discussion section you will have the opportunity to work through additional problems related to the topics with the help of the TAs. You will find these problems posted on ☞ MyOpenMath. This will also be an opportunity for you to receive help on other assignments from your TA. You will also take your retakes in discussion section.

Office Hours

These are an essential resource that often go underutilized. We encourage you to attend them to receive help on any aspect of the course. Find them in the ☞ Office Hours tab.

Math Center

The ☞ USC Math Center (KAP 263) is a place to go if you want help with your math classes. It is open during regular business hours and is always stocked with graduate students who can assist you with your mathematics classes.

Academic Integrity

The University of Southern California is foremost a learning community committed to fostering successful scholars and researchers dedicated to the pursuit of knowledge and the transmission of ideas. Academic misconduct is in contrast to the university's mission to educate students through a broad array of first-rank academic, professional, and extracurricular programs and includes any act of dishonesty in the submission of academic work (either in draft or final form).

This course will follow the expectations for academic integrity as stated in the USC Student Handbook. All students are expected to submit assignments that are original work and prepared specifically for the course/section in this academic term. You may not submit work written by others or "recycle" work prepared for other courses without obtaining written permission from the instructor(s). Students suspected of engaging in academic misconduct will be reported to the Office of Academic Integrity.

Other violations of academic misconduct include, but are not limited to, cheating, plagiarism, fabrication (e.g., falsifying data), knowingly assisting others in acts of academic dishonesty, and any act that gains or is intended to gain an unfair academic advantage.

The impact of academic dishonesty is far-reaching and is considered a serious offense against the university and could result in outcomes such as failure on the assignment, failure in the course, suspension, or even expulsion from the university.

For more information about academic integrity see the student handbook or the Office of Academic Integrity's website, and university policies on Research and Scholarship Misconduct.

Course Content Distribution and Recording Policies

USC has policies that prohibit recording and distribution of any synchronous and asynchronous course content outside of the learning environment.

Recording a university class without the express permission of the instructor and announcement to the class, or unless conducted pursuant to an Office of Student Accessibility Services (OSAS) accommodation. Recording can inhibit free discussion in the future, and thus infringe on the academic freedom of other students as well as the instructor. (Living our Unifying Values: The USC Student Handbook, page 13).

Distribution or use of notes, recordings, exams, or other intellectual property, based on university classes or lectures without the express permission of the instructor for purposes other than individual or group study. This includes but is not limited to providing materials for distribution by services publishing course materials. This restriction on unauthorized use also applies to all information, which had been distributed to students or in any way had been displayed for use in relationship to the class, whether obtained in class, via email, on the internet, or via any other media. (Living our Unifying Values: The USC Student Handbook, page 13).

Students and Disability Accommodations

USC welcomes students with disabilities into all of the University’s educational programs.The Office of Student Accessibility Services (OSAS) is responsible for the determination of appropriate accommodations for students who encounter disability-related barriers. Once a student has completed the OSAS process (registration, initial appointment, and submitted documentation) and accommodations are determined to be reasonable and appropriate, a Letter of Accommodation (LOA) will be available to generate for each course. The LOA must be given to each course instructor by the student and followed up with a discussion. This should be done as early in the semester as possible as accommodations are not retroactive. More information can be found at osas.usc.edu. You may contact OSAS at (213) 740-0776 or via email at osasfrontdesk@usc.edu.

Support Systems

Counseling and Mental Health - (213) 740-9355 24/7 on call

Free and confidential mental health treatment for students, including short-term psychotherapy, group counseling, stress fitness workshops, and crisis intervention.

988 Suicide and Crisis Lifeline - 988 for both calls and text messages 24/7 on call

The 988 Suicide and Crisis Lifeline (formerly known as the National Suicide Prevention Lifeline) provides free and confidential emotional support to people in suicidal crisis or emotional distress 24 hours a day, 7 days a week, across the United States. The Lifeline is comprised of a national network of over 200 local crisis centers, combining custom local care and resources with national standards and best practices. The new, shorter phone number makes it easier for people to remember and access mental health crisis services (though the previous 1 (800) 273-8255 number will continue to function indefinitely) and represents a continued commitment to those in crisis.

Relationship and Sexual Violence Prevention Services (RSVP) - (213) 740-9355 (WELL) – 24/7 on call

Free and confidential therapy services, workshops, and training for situations related to gender- and power-based harm (including sexual assault, intimate partner violence, and stalking).

Office for Equity, Equal Opportunity, and Title IX (EEO-TIX) - (213) 740-5086

Information about how to get help or help someone affected by harassment or discrimination, rights of protected classes, reporting options, and additional resources for students, faculty, staff, visitors, and applicants.

Reporting Incidents of Bias or Harassment - (213) 740-5086 or (213) 821-8298

Avenue to report incidents of bias, hate crimes, and microaggressions to the Office for Equity, Equal Opportunity, and Title for appropriate investigation, supportive measures, and response.

The Office of Student Accessibility Services (OSAS) - (213) 740-0776

OSAS ensures equal access for students with disabilities through providing academic accommodations and auxiliary aids in accordance with federal laws and university policy.

USC Campus Support and Intervention - (213) 740-0411

Assists students and families in resolving complex personal, financial, and academic issues adversely affecting their success as a student.

Diversity, Equity and Inclusion - (213) 740-2101

Information on events, programs and training, the Provost’s Diversity and Inclusion Council, Diversity Liaisons for each academic school, chronology, participation, and various resources for students.

USC Emergency - UPC: (213) 740-4321, HSC: (323) 442-1000 – 24/7 on call

Emergency assistance and avenue to report a crime. Latest updates regarding safety, including ways in which instruction will be continued if an officially declared emergency makes travel to campus infeasible.

USC Department of Public Safety - UPC: (213) 740-6000, HSC: (323) 442-1200 – 24/7 on call

Non-emergency assistance or information.

Office of the Ombuds - (213) 821-9556 (UPC) / (323) 442-0382 (HSC)

A safe and confidential place to share your USC-related issues with a University Ombuds who will work with you to explore options or paths to manage your concern.

Occupational Therapy Faculty Practice - (323) 442-2850 or otfp@med.usc.edu

Confidential Lifestyle Redesign services for USC students to support health promoting habits and routines that enhance quality of life and academic performance.