Description

An introduction to probability and statistics for engineers, with an emphasis on modeling and reasoning about uncertainty. Topics include:

  • Sample spaces and probabilistic models
  • Discrete random variables
  • General random variables
  • Further topics on random variables
  • Limit theorems
  • Basic statistical inference

Learning outcomes

By the end of the course, you will be able to:

  • Build probabilistic models of engineering systems and phenomena affected by uncertainty.
  • Compute probabilities, distributions, and expectations, and reason correctly about conditioning, independence, and dependence.
  • Analyze the behavior of large collections of random variables using limit theorems.
  • Draw conclusions from data by estimating parameters and testing hypotheses.

Prerequisites

  • Basic with mathematical reasoning (logical implications and basic proof techniques)
  • Basic set theory (set cardinality and operations)
  • Multivariate calculus (differentiation and integration)
  • Basic linear algebra (vectors and matrices)

Enrollment is open to Electrical Engineering, Computer Engineering, and pre-Computer Engineering majors only. Students from other majors who are interested in enrolling should reach out to the instructor.

Instructors

Main instructor:

  • Tobia Marcucci
  • Email: marcucci@ucsb.edu
  • Office: Harold Frank Hall, room 5155

Teaching assistant:

  • Jonathan Lane
  • Email: jglane@ucsb.edu
  • Office: Harold Frank Hall, room 5156

Lectures

  • Tuesday and Thursday from 2:00pm to 3:15pm (starting September 24)
  • Room 1701, Theater & Dance West (TD-W)

Discussion sections

Discussion sections are led by the teaching assistant and are devoted to solving problems and reviewing the material covered in lecture.

  • Wednesday from 6:00pm to 7:50pm, room ILP 4105
  • Friday from 12:00pm to 1:50pm, room ILP 4103

Office hours

  • Monday 3pm to 4pm (by Jonathan in Harold Frank Hall 5152)
  • Wednesday 2pm to 3pm (by Tobia in Harold Frank Hall 5155)

The instructors will also be available for questions at the end of each lecture and discussion section.

Textbook

The course will follow closely the book Introduction to Probability, 2nd edition, by Dimitri P. Bertsekas and John N. Tsitsiklis. The book can be purchased at the University bookstore or online. Supplementary material (including a pdf copy of the first chapter, solved problems, additional exercises, and recorded lectures) is freely available on the authors’ book page. See also the MIT OpenCourseWare page for 6.041 for additional resources.

Numerous other excellent books cover the same sequence of topics at different levels of mathematical depth. I encourage you to explore them if you find the one used in the class unclear (too advanced, too simple, lacking examples, lacking theory, etc.).

Homework

  • Practice exercises will be released on Canvas approximately every week, but they will not be graded. Nothing has to be submitted.
  • Complete solutions will be posted on Canvas together with each assignment.
  • Although the homework does not contribute to your grade, it is one of the most important parts of your work in this class. Probability is learned by solving problems, and the exam problems will be very similar in style and difficulty to the homework ones. Students who do not work through the assignments on their own, before looking at the solutions, should not expect to do well on the exams.
  • You are strongly encouraged to attempt every problem before the solutions are released, and to bring the ones you could not solve to the discussion sections or to office hours.

Exams

The course will have two midterm exams and one final exam:

  • Midterm 1: Thursday, October 20 from 2:00pm to 3:15pm in TD-W 1701.
  • Midterm 2: Tuesday, November 17 from 2:00pm to 3:15pm in TD-W 1701.
  • Final: Tuesday, December 8 from 4:00pm to 7:00pm in TD-W 1701.

Exam rules:

  • Exams will be closed book and closed notes. You may bring a cheat sheet in your own handwriting, consisting of a single two-sided sheet (letter size). A new cheat sheet may be prepared for each exam.
  • No calculators, personal computers, tablets, or cellphones are allowed during the exams.
  • If you have a documented conflict with one of the exam dates, or you require special accommodations, please contact the instructor as early as possible in the quarter.

Grading

Your grade will be assigned roughly according to the following weights:

  • Midterm 1: 20%
  • Midterm 2: 30%
  • Final: 50%

Please note that these weights are approximate, and we reserve the right to change them later.

Academic integrity

We adhere to the UCSB Academic Integrity Policy.

Lecture schedule

The lectures will roughly follow the textbook. After each lecture, we will summarize below the material covered (relevant sections of the book, plus any additional material).

  • Lecture 1 (September 24)
  • Lecture 2 (September 29)
  • Lecture 3 (October 1)
  • Lecture 4 (October 6)
  • Lecture 5 (October 8)
  • Lecture 6 (October 13)
  • Lecture 7 (October 15)
  • Midterm 1 (October 20)
  • Lecture 8 (October 22)
  • Lecture 9 (October 27)
  • Lecture 10 (October 29)
  • Lecture 11 (November 3)
  • Lecture 12 (November 5)
  • Lecture 13 (November 10)
  • Lecture 14 (November 12)
  • Midterm 2 (November 17)
  • Lecture 15 (November 19)
  • Lecture 16 (November 24)
  • Thanksgiving (no lecture on November 26)
  • Lecture 17 (December 1)
  • Lecture 18 (December 3)
  • Final (December 8)

Tentative homework schedule

  • Homework 1: released on October 1
  • Homework 2: released on October 8
  • Homework 3: released on October 20
  • Homework 4: released on October 27
  • Homework 5: released on November 3
  • Homework 6: released on November 12
  • Homework 7: released on November 19
  • Homework 8: released on December 1