Pierre Perruchaud

Introduction to Probability

This page has been amended after the end of the course, and remains online solely for illustration purposes.

Probability is the mathematical study of random phenomena. It has been stunningly efficient in helping us understand matters as diverse as the development of early civilisation, the number of horse-kick related deaths in the Prussian military (!) or the behaviour of magnetic materials, to name but a few. Nowadays, probability skills are sought after for instance in the insurance industry, or in the field of machine learning and neural networks. Of course, the less grounded of us will learn for the sheer fun of it!

The official course description reads as follows: “An introduction to the theory of probability, with applications to the physical sciences and engineering. Topics include discrete and continuous random variables, conditional probability and independent events, generating functions, special discrete and continuous random variables, laws of large numbers and the central limit theorem. The course emphasises computations with the standard distributions of probability theory and classical applications of them.”

At the end of this course, you will be able to

  • define and manipulate the basic objects of probability theory;
  • compute the probability of events, given appropriate probability distributions;
  • model real life situations using appropriate probability distributions;
  • apply the Central Limit Theorem when estimating probability distributions and determining sample size;
  • prove facts from probability requiring techniques from calculus (i.e. series convergence and integration).
In short, you will be ready for basic applications of probability theory, for instance in statistics, and to expand your knowledge on your own if needed.

Practical information

Class time: 1:00 to 1:50, Monday Wednesday Friday, in Hayes-Healy 127.

Zoom meeting: the meeting ID is 983 6823 3401 . The password to access the room is available on Sakai.

Instructor contact: Pierre Perruchaud, , Hayles-Healy 202.

Office hours: 2:30 to 3:30 on Mondays, 10:30 to 11:30 on Thursdays, or by appointment. These office hours are remote. The Zoom meeting ID is 944 2755 7165, and the password is available on Sakai.

Resources

Textbook: Notes on Elementary Probability, Liviu I. Nicolaescu. [pdf] [Amazon]
Professor Nicolaescu kindly makes his book freely available to the students of Notre Dame.

Website: On this very page, you will find up-to-date information, such as the assigned homework and useful documents.

Main topics: As we go along, I will compile a list of key notions and relevant exercises for the different topics we cover in class.

Course grade

There will be four types of evaluations, described in the next paragraph:

  • homework (100 points)
  • quizzes (100 points)
  • two midterms (100 points each)
  • a final (150 points)
for a total of 550 points.

The scale will be roughly 90% for A or A-; 75% for B+, B or B-; 65% for C+, C or C-.

Homework

Homework will be announced most Fridays and posted on this website. It will be due at the beginning of class the following Friday, most likely on Gradescope.

Each assignment will involve some reading and some problems, possibly on an area not yet covered in lectures. Presented assignments should be neat and legible. Write your name and the assignment number legibly at top of the first page. The grader reserves the right to leave ungraded any assignment that is disorganised, untidy or incoherent. Late assignments will be graded for half the points. It is permissible (and encouraged) to discuss the assignments with your colleagues, but the writing of each assignment must be done on your own.

Previous homework:

In-class evaluations

Quizzes will be held on Wednesdays about four times in the semester. They are done in class, and collaboration is prohibited. You will be given 15 minutes.

Previous quizzes:

There will be two midterms, done in class, of 50 minutes each. Collaboration is again prohibited. They are scheduled on March 15th and April 19th.

The exam is scheduled on Tuesday the 18th of May, from 8:00AM to 10:00AM. For practice, you can refer to the review sheets for Midterm 1 and Midterm 2, as well as that of the last class.

Honour code

You have all taken the Honour Code pledge, to not participate in or tolerate academic dishonesty. For this course, that means that although you may discuss homework assignments with your colleagues, you must complete each assignment yourself, all work that you present in quizzes and exams must be your own, and you will adhere to all announced exam policies.

Health and Safety

As part of the collective effort to maintain a healthy environment in Notre Dame, in this class I will ask you to observe the following policies.

  • Wear a face mask that completely covers the nose and mouth.
  • When the time comes, register your seat at here.nd.edu/seat, and sit in your assigned seats throughout the semester.
  • Complete your daily health check.
  • Participate in surveillance testing.
  • More generally, comply to the university policies, as described on the HERE website.

This is a difficult situation we are dealing with. Now more than ever, I am concerned about my students' mental health. Should you feel the need, the Emotional Support and Well-being Group gathered resources on their HERE section, you can reach out to a Care and Wellness Consultant at care.nd.edu, and a few more health initiatives are described on the Division of Student Affairs' webpage. Although I am not a medical professional, know that my door is always open, virtually if needed.