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
- 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 tuesday after class.
The assignment is given in the attached calendar.
Rules for the homework:
The assignment is given in the attached calendar.
Rules for the homework:
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Steps must be shown to explain your answers.
No credit will be given for just writing down the answers, even if it is correct. - Please staple all loose sheets of your homework to prevent 5% penalty.
- If HW submitted through Gradescope, please submit each problem separately on a different page to prevent 5% penalty.
- Please resolve any error in the grading (hws and tests) WINTHIN ONE WEEK after the return of each homework and exam.
- No late homeworks are accepted (in principle).
- 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 on Feb. 24, 8-9pm, in MATH 175.
Program: Chapter 1, Chapter 2, Chapter 3.
A cheat sheet is authorized. It should be handwritten, at most 2 pages long, with formulae only.
This is a link to a Spring 19 Midterm
Here is another Fall 18 Midterm, from a MA519 course
This link sends you to our Review session
Program: Chapter 1, Chapter 2, Chapter 3.
A cheat sheet is authorized. It should be handwritten, at most 2 pages long, with formulae only.
This is a link to a Spring 19 Midterm
Here is another Fall 18 Midterm, from a MA519 course
This link sends you to our Review session
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Final exam
Date: To be taken between 5/6 - 12:00am and 5/7 - 11:59pm. Through Gradescope. 70mn long.
Program: Chapter 4, Chapter 5, Chapter 6.
This link sends you to our Review session together with some Solutions
This is a link to a Spring 19 Final
Here is a Fall 18 Final, from a MA519 course
Program: Chapter 4, Chapter 5, Chapter 6.
This link sends you to our Review session together with some Solutions
This is a link to a Spring 19 Final
Here is a Fall 18 Final, from a MA519 course
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Office hours
12:00-1:30pm on Thursday, in Math 434.
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Slides (Feedback on typos appreciated)
- Ground rules
- Combinatorial analysis
- Axioms of probability
- Conditional probability and independence
- Random variables
- Continuous random variables
- Jointly distributed random variables
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Material for virus times
- Test lecture and Document with computations
- Random variables Section 8 (1) and Document with computations
- Random variables Section 8 (2) and Document with computations
- Random variables Sections 9-10 and Document with computations
- Continuous random variables Section 1 and Document with computations
- Continuous random variables Section 2 and Document with computations
- Continuous random variables Section 3 and Document with computations
- Continuous random variables Section 4 (1) and Document with computations
- Continuous random variables Section 4 (2) and Document with computations
- Continuous random variables Section 5 and Document with computations
- Continuous random variables Section 6 and Document with computations
- Continuous random variables Section 7 and Document with computations
- Jointly distributed random variables Section 1 (1) and Document with computations
- Jointly distributed random variables Section 1 (2) and Document with computations
- Jointly distributed random variables Section 2 and Document with computations
- Jointly distributed random variables Section 3 and Document with computations
- Jointly distributed random variables Section 4 and Document with computations
- Jointly distributed random variables Section 5 and Document with computations
- Jointly distributed random variables Section 6 and Document with computations
- Review session and Document with computations
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