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Introduction to Probability Theory
MA 416
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Introduction
Probabilistic tools are ubiquitous in modeling for engineering, biology and finance. This course proposes an in-depth introduction to the basic mechanisms in probability theory. We begin with a review of the basic uniform probability model on finite spaces and related counting techniques. Next we will introduce the fundamental axioms of probability and study conditional probabilities. Then we shall focus on different types of random variables: discrete, continuous and vector valued random variables.
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Bibliography
  1. S. Ross: A first course in probability. Tenth edition. Pearson, 2018.
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Homework
The homework will be taken from Ross' book. Homeworks are usually due on Friday at 11:59pm.
The assignment is given in the attached calendar.

Rules for the homework:
  1. Steps must be shown to explain your answers.
    No credit will be given for just writing down the answers, even if it is correct.
  2. If HW submitted through Gradescope every Friday before 11:59pm, please submit each problem separately on a different page to prevent 5% penalty.
  3. Please resolve any error in the grading (hws and tests) WINTHIN ONE WEEK after the return of each homework and exam.
  4. No late homeworks are accepted (in principle). Don't start uploading on Friday at 11pm or later!
  5. You are encouraged to discuss the homework problems with your classmates but all your handed-in homeworks must be your own work.
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Midterm
Our midterm will be an evening exam, beginning of March. 1 hour long.
Program: Chapter 1, Chapter 2, Chapter 3, maybe part of Chapter 4.
A cheat sheet is authorized. It should be handwritten, at most 2 pages long, with formulae only.
This link sends you to my Spring 2020 review session together with some Solutions
Here is the Spring 2020 Midterm
This is the Fall 2024 Midterm review session
Here is the Fall 2024 Midterm together with some Solutions
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Final exam
Date: During Finals week. 1 hour long.
Program: Chapter 4, Chapter 5, Chapter 6, part of Chapter 8 (at least problems 8.5 and 8.14).
This link sends you to our Spring 2020 review session together with some Solutions
Here is my Spring 20 Final and the Solution to Problem 5
Here is my Fall 24 Final and the Solutions
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Office hours
12pm-1:30pm on Monday, by Zoom.
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Syllabus
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Slides (Feedback on typos appreciated)
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Documents with computations (notes from lectures)
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