# TEXTBOOK

Mor is completing a textbook that is customized for this class. The book is going to be printed and bound. We hope to give out this book to you on the first day of class. The book is self-contained and is free to you, courtesy of Citadel. You do not need to purchase any other resources for the class.

# PREREQUISITES

15-259 assumes NO PRIOR PROBABILITY/STATS classes, and will satisfy
the Computer Science Probability/Statistics requirement. The course
DOES assume that you have taken calculus (and still remember how to
integrate, differentiate, and do Taylor-series expansions). The
course also assumes that you can do double integrals, including
changing the order of integrals, and also know some basic matrix
algebra (eigenvectors, solving equations, etc.). The main
prerequisite is 15-251, where we expect that you learned how to sum
basic arithmetic and geometric series and got some practice with basic
combinatorics/counting as well as receiving some exposure to
algorithms. (If you are a math major, we're happy to accept 21-228 instead of 15-251). Prior classes in 3D Calculus and Linear Algebra are
highly recommended, and are listed as prerequisites.
Homework 0 is a ** Prerequisite Review **.
It is due on the first Friday after the start of class -- Jan 21 -- at 1 p.m. sharp, on Gradescope.

# STUDENT WELLNESS

If you are experiencing distress (mentally, physically, or emotionally) that is making it impossible for you to work, we want to hear about it. Please reach out to us so we can meet and talk:
harchol@cs.cmu.edu, weinaw@cs.cmu.edu.
Some other resources:

- Counseling and Psychological Services: 412-268-2922
- Re:solve Crisis Network: 888-796-8226
- If the situation is life threatening, call the police:
On campus (CMU Police): 412-268-2323. Off campus: 911.

# 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, Chebyshev, and Chernoff bound concentration inequalities.

- Design randomized algorithms and analyze their efficiency.

- Model problems using discrete-time and continuous-time Markov chains.

- Derive limiting probabilities of Markov chains.

- Construct and analyze models for performance analysis of queueing networks.

- Understand the application of probability to problems in machine learning, theoretical computer science, networking, cloud computing, and operations research.

# CHEATING POLICY

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.
All work in quizzes and exams must be done entirely by you with zero consultation from other sources (people, web, texts, etc.), unless otherwise instructed.