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 emphasizes 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: 12:50 to 1:40, Monday Wednesday Friday, in Hayes-Healy 129.

Instructor contact: Pierre Perruchaud, .

Office hours: 10:00 to 11:30 on Mondays, 10:00 to 11:30 on Thursdays.

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.

Simulations: I will write a few simulations during this class, through my Observable profile.

If you spot mistakes or have constructive criticism on any of the above items, please let me know by clicking the envelope at the bottom of the page.

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-; 60% 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.

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, the course number and the assignment number legibly at top of the first page. If you use more than one page, you should staple all your pages together. The grader reserves the right to leave ungraded any assignment that is disorganized, 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 once or twice a month. They are done in class, and collaboration is prohibited. You will be given 15 minutes.

Previous quizzes:

The final exam will consist in oral evaluations, to be held during the week of the May 4th. You have to choose a topic we will spend particular attention to, from the following list.

  1. Probability spaces, events, conditioning
  2. Counting
  3. Discrete variables, multivariate discrete variables
  4. Continuous variables
  5. Multivariate continuous variables
  6. Variance, moments, inequalities, limit theorems
You will find more details about what they entail by refering to this document. It should also give you an idea of what will be evaluated outside this particular focus.

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 WebAssign assignment yourself, all work that you present in quizzes and exams must be your own, and you will adhere to all announced exam policies.