DS6300

Theory I: Probability & Stochastic Processes - Fall 2025

Course information


Course materials

Additional Resources


Topics

  1. Foundations of probability
    • Events and probability spaces
    • Conditional probability
    • Independence
  2. Random variables
    • Probability distributions
    • Expectation, variance, and moments
    • Multiple random variables, covariance, and correlation
  3. Limit theorems
    • Sums of random variables
    • Law of large numbers
    • Central limit theorem
  4. Stochastic processes
    • Markov processes
    • Poisson processes
  5. Tail bounds
    • Concentration inequalities
    • Sub-Gaussian and sub-exponential distributions

Schedule

Aug 27 2025: Course overview

Sep 01 2025: Probability spaces

Sep 03 2025: Probabilistic reasoning

Sep 08 2025: Random variables

Sep 10 2025: Distribution functions

Sep 15 2025: Multiple random variables, Buffon’s needle

Sep 17 2025: Independence and common random variables

Sep 22 2025: Practice problems, mean and variance

Sep 24 2025: Mean, variance, and moment derivations

Sep 29 2025: Moments of random variables

Oct 01 2025: Moment generating functions

Oct 06 2025: Weak law of large numbers

Oct 08 2025: Central Limit Theorem

Oct 13 2025: Fall reading day (no class)

Oct 15 2025: Conditional densities, conditional expectation

Oct 20 2025: Midterm review

Oct 22 2025: Midterm exam [Solutions]

Oct 27 2025: Conditional probability, simulation

Oct 29 2025: Markov chains

Nov 03 2025: Markov chain examples, autocorrelation

Nov 05 2025: Aperiodicity, irreducibility, and the Ergodic Theorem

Nov 26 2025: Thanksgiving recess (no class)

Dec 13 2025: Final exam (2:00 - 5:00 pm Data Science Building 246)


Grades

Final grades will be computed using the following weighting of assignments and exams:

Grading scale:

Note that a B- is the lowest satisfactory grade for graduate credit.

Course Policies

Submitting Homework

Homework will be accepted through the Assignments page on Canvas. Submissions will be in PDF format. You may hand-write and scan problem solutions, or you may use a typesetting software like LaTeX, Markdown, etc. Some homework assignments will involve using code to produce graphical or numerical outputs and will require the use of software. Please compile all materials in a single PDF for submission and make sure that whatever you have written can be clearly read by the grader.

Grades for (on-time) homework will be made visible to students no later than one week after the assignment due date. Grades for late work (see below) will become available as time permits.

Late Work Policy

The expectation in this course is that all assignments will be submitted on time. Submitting your work on time respects the efforts of your instructor and teaching assistant, and it ensures that you are prepared to learn subsequent material.

Assignments turned in after the due date incur a 10% penalty per late day. For example, an assignment due at 9:30 am on Wednesday that is submitted to Canvas at 3:00 pm on Friday will incur a 30% penalty. If the assignment would have received a 95% had it been returned on time, then the late grade is 65%. Note that weekend days count towards the late penalty.

I will not accept work that is late by more than one week past its due date.

To provide flexibility for weeks in which life circumstances do not permit the completion of your coursework, your lowest homework grade will be dropped. Additionally, your two lowest reading quiz grades will be dropped.

Class Attendance

Attendance in this class is mandatory. If you need to miss a class for any reason, please email me in advance. You are responsible for keeping up with the lecture material, but I am happy to work with you during office hours or by appointment to brush up on things you may have missed.

Extenuating Circumstances

Students are expected to communicate with me as soon as possible regarding extenuating circumstances and how their participation in the course, including attendance and assignment submissions, may be affected by them.

University Support and Policies