## Course Information

### Description

Probability is a mathematical discipline for reasoning about randomness -- it helps us make decisions in the face of uncertainty and build better systems. In this course, we will teach you the fundamental ideas of probability and random processes. The various assignments are carefully designed to strengthen your mathematical understanding of probability and to demonstrate how these concepts can be applied to the real world, be it in communication networks, control systems, or machine learning.

### Prerequisites

Knowledge of probability at the level of CS 70, Stat 134, or Stat 140; linear algebra at the level of EECS 16A or Math 54.

### Course Outline

- Fundamentals of Probability / 4 weeks
- Review of probability basics and common distributions
- Transforms of random variables, concentration inequalities
- Convergence, law of large numbers, central limit theorem

- Information Theory and Random Processes / 5 weeks
- Information theory
- Discrete time Markov chains
- Poisson processes
- Continuous time Markov chains

- Estimation and Hilbert Space of Random Variables / 4 weeks
- Maximum likelihood estimate, maximum a posteriori estimate, hypothesis testing
- Hilbert space of random variables
- LLSE estimate, MMSE estimate
- Jointly Gaussian random variables and Kalman filter
- Hidden Markov models

### Textbooks

The course will follow the B&T textbook, as well as the new Walrand textbook which you can find here.

- Dimitris P. Bertsekas and John N. Tsitsiklis, Introduction to Probability, 2nd Edition, Athena Scientific, 2008.
- Jean Walrand, Probability in Electrical Engineering and Computer Science: An Application-Driven Course, Springer, 2021.

### Ed

We will be using Ed for class discussion. Rather than emailing questions to the GSIs, we encourage you to post your questions on Ed. If you can't access the course, please contact course staff at eecs126-fall23 (at) lists.eecs.berkeley.edu.

### Expectations Regarding Conduct Online

It shouldn't have to be said, but please keep your online posts constructive, respectful, and course-related. We want Ed Discussion to be a resource that promotes a positive and inclusive culture for learning and collaboration. Trolling, rants, or other abusive behavior that does not contribute to this goal won't be tolerated, and may result in revocation of your forum privileges. In short, keep it professional.

### Gradescope

We will use Gradescope for all submissions/grade-related items. If you are not added automatically, please use the code NX6735 to join. Note that our policy for accepting assignments (not exams) is that if Gradescope accepts the assignment, it is accepted, even if it says late or assigns a late timestamp.

### Grading

The grading breakdown is as follows:

- Homework (15%)
- Lab (10%)
- Midterm 1 (20%)
- Midterm 2 (20%)
- Final (35%)

### Exams

We will be using a clobber policy where your final can replace your grade for either MT1 or MT2, but not both.

In situations that will foreseeably result in a need for accommodation, make a private Ed post.

See the exams page for more details.

### Homework

- Homeworks will be posted on the course website every Saturday morning and are due on the following Friday at 10:59 PM.
- Homeworks should be submitted as a PDF to Gradescope.
- Any homework that is illegible or too difficult to read will get a 0.
- Homeworks will be self-graded through Gradescope. The assignments will open every Saturday morning and due the next Friday at 10:59 PM.
- You will have a 1 hour grace period to submit the homework and self-grade. No late self-grades or homework submissions will be accepted after that.
- You will only recieve a score for your homework if you turn in BOTH your homework and your self-grade on time.
- Your lowest homework score will be dropped automatically.
- You will have the opportunity for two extra homework drops by answering mid-semester surveys.
- Your homework grades are given by 1.25 x min(your self grade, .8), i.e. the max score is 80%.

### Labs

- Labs will be posted on the course website every Wednesday morning and are due on the following Tuesday at 10:59 PM.
- Labs will be in the form of Jupyter notebooks. Students should submit these notebooks as a .pdf to Gradescope.
- Labs will be self-graded through Gradescope. The assignments will open every Wednesday morning and are due on the following Tuesday at 10:59 PM.
- You will have a 1 hour grace period to submit the lab and self-grade. No late self grades or lab submissions will be accepted after that.
- You will only recieve a score for your lab if you turn in BOTH your lab and your self-grade on time.
- Your lowest lab score will be dropped automatically.
- You will have the opportunity for two extra lab drops by answering mid-semester surveys.

### Self-Grading Policy

We will periodically be checking self-grades internally to ensure that they are accurate. If we find that your self-grades do not align with our scores (either positively or negatively), we will reach out to you and adjust your self-grades. Please remember the Academic Dishonesty policy and the Berkeley honor code and try to report your self-grades accurately.

Each problem is worth 4 points:

- 4: fully correct
- 3: minor mistakes, close to correct solution
- 2: major mistakes, incorrect direction
- 1: little progress
- 0: not attempted

For problems with subparts, we will specify the breakdown; apply to rubric similarly to each subpart.

### Collaboration

You are encouraged to discuss homework and lab assignments with your classmates. However, you must always write up the solutions on your own, and you must never copy the solutions of other students. Similarly, you may use books or online resources to help solve homework problems, but you must credit all such sources in your writeup and you must never copy material verbatim. You are reminded of the Department's Policy on Academic Dishonesty. In particular, you should be aware that copying solutions, in whole or in part, from other students in the class or any other source without acknowledgment constitutes a violation of this policy and risks serious consequences.

### Policy on Course Content

The University's Policy on Classroom Note-Taking and Recording applies to this course. You are free and encouraged to use course materials for personal use (in collaborations with other students, in your research, etc.). You are also granted permission to post any notes you create on your own personal website. You are expressly prohibited from publicly uploading course materials created by teaching staff (exams, HW, solutions, labs). In particular, any upload of course content to websites such as CourseHero.com or Chegg.com, which distribute and monetize content without permission from the instructor or University will be considered a violation of University Policy, and referred to the Center for Student Conduct.