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Probability and Computing (PnC)

CMU 15-259 | 15-559 FALL 2025

PnC: where probability meets chocolate!

Instructors: Feras Saad and Weina Wang
Location: Doherty Hall (DH) 2315
Date and Time: Tuesday / Thursday, 14:00–15:20
Contact: pnc-instructors@cs.cmu.edu

Course Info

Probability theory is indispensable in computer science:

• It is at the core of artificial intelligence and machine learning, which require decision making under uncertainty.
• It is integral to CS theory, where probabilistic analysis and randomization form the basis of many algorithms.
• It is a central part of performance modeling in computer networks and systems, where probability is used to predict delays, schedule resources, and provision capacity.

This course gives an introduction to probability as it is used in computer science theory and practice, drawing on applications and current research developments as motivation and context.

Key Topics: probability on events, discrete and continuous random variables, conditioning and Bayes, higher moments, Laplace transforms and z-transforms, Gaussians and central limit theorem, tails and stochastic dominance, heavy-tailed distributions, Poisson processes, simulation of random variables, estimators for mean and variance, maximum likelihood estimation (MLE). MAP estimation, Bayesian statistics, confidence intervals.

Learning Outcomes

• Analyze probabilities and expectations using tools such as conditioning, independence, linearity of expectations
• Compute expectation and variance of common discrete and continuous random variables
• Apply z-transforms and Laplace transforms to derive higher moments of random variables
• Prove elementary theorems on probability
• Analyze tail probabilities via Markov and Chebyshev inequalities
• Generate random variables for simulation
• Perform simulations of Poisson arrival processes as well as event-driven simulations.
• Compute sample estimators for mean and variance.
• Derive estimators for statistical inference, including MLE, MAP, and Bayesian estimators.
• Understand the application of probability to problems in machine learning, theoretical computer science, networking, cloud computing, and operations research.

Prerequisite Knowledge

What prior knowledge must students have in order to be successful in this course?

PnC does not assume any background in probability or statistics, and will satisfy the probability and statistics requirement for Computer Science and AI Majors in SCS.

The course does assume knowledge of calculus (e.g., single and double integrals, differentiation, Taylor-series expansions), discrete mathematics (e.g., sequences, combinatorics, asymptotic notation), and proof writing. CMU courses that satisfy the prerequisites are listed below; contact the instructors if you may have taken a different course that fulfills the requirement.

Multivariable Calculus: 21-268 or 21-266 or 21-259 or 16-211
Discrete Mathematics: 21128 or 21127 or 15251 or 15151

Diagnostic Test: Students who have met the prerequisites but are still unsure of their preparation should take the PnC self-diagnostic test. to help identify gaps in their background: If you have completed the self-diagnostic and wish to check your answers, email pnc-instructors@cs.cmu.edu for solutions.

Textbook

Schedule

Lectures

Lecture handouts will be posted to Canvas prior to lecture.

Lecture 1	Tue Aug 26	Chapter 2	Saad
Lecture 2	Thu Aug 28	Chapter 3	Saad
Lecture 3	Tue Sep 2	Chapter 3-4	Saad
Lecture 4	Thu Sep 4	Chapter 4	Saad
Lecture 5	Tue Sep 9	Chapter 5	Saad
Lecture 6	Thu Sep 11	Chapter 5	Saad
Lecture 7	Tue Sep 16	Chapter 5	Saad
Lecture 8	Thu Sep 18	Chapter 6	Saad
Lecture 9	Tue Sep 23	Chapter 7	Wang
Lecture 10	Thu Sep 25	Chapter 7-8	Wang
Lecture 11	Tue Sep 30	Chapter 8	Wang
Lecture 12	Thu Oct 2	Chapter 8	Wang
No Class	Tue Oct 7	Midterm 1	17:00–19:00, PH 100
Lecture 13	Thu Oct 9	Chapter 9	Wang
No Class	Tue Oct 14	Fall Break
No Class	Thu Oct 16	Fall Break
Lecture 14	Tue Oct 21	Chapter 10	Wang
Lecture 15	Thu Oct 23	Chapter 11	Wang
Lecture 16	Tue Oct 28	Chapter 12	Saad
Lecture 17	Thu Oct 30	Chapter 12	Wang
No Class	Tue Nov 4	Democracy Day
Lecture 18	Thu Nov 6	Chapter 13	Wang
Lecture 19	Tue Nov 11	Chapter 15	Saad
No Class	Thu Nov 13	Midterm 2	17:00–19:00, PH 100
Lecture 20	Tue Nov 18	Chapter 16	Saad
Lecture 21	Thu Nov 20	Chapter 16	Saad
Lecture 22	Tue Nov 25	Chapter 17	Wang
No Class	Thu Nov 27	Thanksgiving
Lecture 23	Tue Dec 2	Chapter 18	Wang
Lecture 24	Tue Dec 4	Chapter 19.1–19.3	Wang

Recitations

Section A: Friday 09:00–09:50, GHC 5222
Section B: Friday 13:00–13:50, BH 255A
Section C: Friday 13:00–13:50, GHC 4102
Section D: Friday 14:00–14:50, BH 255A
Section E: Friday 09:00–09:50, PH A18A
Section F: Friday 13:00–13:50, PH A18A
Section G: Friday 14:00–14:50, PH A18A

Homework

Homework is due each week on Friday at 12:50pm on GradeScope. There are no extensions or exceptions. The lowest homework score will be dropped.

• Homework 1, due 08/29/2025
• Homework 2, due 09/05/2025
• Homework 3, due 09/12/2025
• Homework 4, due 09/17/2025

Staff

Professors

Feras Saad	Weina Wang

NOTE: To ensure a timely response, all emails to the professors should be sent to pnc-instructors@cs.cmu.edu

Teaching Assistants

Allen Yang allenyan@andrew.cmu.edu	Dustin Miao dustinmi@andrew.cmu.edu
George Liu georgeli@andrew.cmu.edu	Grace Wang gracewan@andrew.cmu.edu
Hari Desikan hdesikan@andrew.cmu.edu	Junzhao Yang junzhaoy@andrew.cmu.edu
Megha Narayanan meghanar@andrew.cmu.edu	Pranav Sangwan psangwan@andrew.cmu.edu
Raj Maheshwari rajmahes@andrew.cmu.edu	Rohan Jain rohanjai@andrew.cmu.edu
Jenny Quan jennyq@andrew.cmu.edu	Kevin Zhang kz3@andrew.cmu.edu

Office Hours

Please refer to the following map of the GHC 5th Floor for information on the Carrel and Table numbers.

Policies

Grading

All assignments, quizzes, and exams will be graded on Gradescope.

Grade Components: The final grade is computed as follows:

• Homework: 15%
• In-Class Quizzes: 15%
• Midterm 1: 20% or 25% (see note)
• Midterm 2: 20% or 25% (see note)
• Final: 25%

The lower midterm score will be weighted by 20% and the higher midterm score will be weighted by 25%. The lowest homework score and two lowest quiz scores will be dropped. Please reserve these drops for when you get sick or have another conflict, because there are no makeups or extensions for homework or quizzes.

For In-Class Quizzes, students with disability accommodations have the option to either (a) take the quizzes during the usual lecture time without accommodations, with the 3 lowest scores dropped; or (b) distribute the 15% component equally among Midterm 1 (25% or 30%), Midterm 2 (25% or 30%), and Final (30%). Students must make this election before Quiz 3.

Grade Boundaries: A: 90–100%, B: 80–90%, C: 70–80%, D: 60–70%. These boundaries are hard cutoffs. Do not expect an overall curve at the end. Individual quizzes or examinations may be curved at the instructor's discretion.

Lateness: Homework will go out each week on Friday. When the homework goes out, you already have all the material you need to do it that day. Homework will be due each week the following Friday at 12:50 (midday) sharp. Start right away! You must get the homework in on time because we give out solutions during recitation. There are no late days (not even late minutes). Please do not ask for these. Homework is graded within a couple days. You can submit a regrade request on Gradescope (including a detailed explanation of why you think you were misgraded) within two days of when you get your homework grade. You will find the homework under the Homeworks tab from the class website. You will turn in homework on Gradescope, which will also track your grades.

Cheating

PnC admits a zero-tolerance policy on cheating. All quizzes and exams must be done entirely by you with zero consultation from unauthorized sources (e.g., people, web, texts). Any incident of cheating during a quiz, midterm, or final will result in a failing grade for the entire course, and referral to the Office of Community Responsibility for an Academic Integrity Violation proceedings. Students should familiarize themselves with the University Policy on Academic Integrity and Academic Integrity Actions Procedures chapter of the Student Handbook.

Collaboration

We believe in collaboration. Discussing problems with others helps you learn better. If you collaborate with others, try to get "hints" rather than "answers." You should write up your actual homework on your own. If you use an outside source (web site, book, person, etc.), you must cite that source. At the top of your homework sheet, you must list all the people with whom you discussed any problem. Even if you were the one doing the helping, you should list the other person. Crediting discussion with others will not take away any credit from you, and will prevent us from assuming cheating if your answers look similar to those of someone else. The above is the standard policy in all of academia.

Assisted Tools

We recognize that some students may solve homework problems by consulting previous solutions, online resources, or generative AI tools such as large language models (LLMs). Our course policy is that these resources should not be used to complete homework problems. Using these resources will significantly impair your ability to meet the course learning objectives, learn how to solve novel problems outside the textbook, and lead to noticeable performance gaps in the quizzes and examinations (which comprise the majority of your course grade).

Wellbeing

If you are experiencing distress (mentally, physically, or emotionally) that is making it difficult for you to work and make progress in the class, we are here to help you. Please reach out to Feras or Weina so we can meet and discuss.

Calendar

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