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 an evening exam, on October 16, 8-9pm, in KRAN G016 and RAWL 1086. 1 hour long.
Program: Chapter 1, Chapter 2, Chapter 3, Chapter 4 (Sections 4.1, 4.2, 4.3, 4.4, 4.5).
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
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
Program: Chapter 1, Chapter 2, Chapter 3, Chapter 4 (Sections 4.1, 4.2, 4.3, 4.4, 4.5).
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
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: Dec 10, from 3:30 to 4:30pm. 1 hour long. Room: PHYS 112
Program: Chapter 4, Chapter 5, Chapter 6, plus problems 8.5 and 8.14.
This link sends you to our Spring 2020 review session together with some Solutions
This is a link to a Spring 19 Final
Here is my Spring 20 Final and the Solution to Problem 5
Program: Chapter 4, Chapter 5, Chapter 6, plus problems 8.5 and 8.14.
This link sends you to our Spring 2020 review session together with some Solutions
This is a link to a Spring 19 Final
Here is my Spring 20 Final and the Solution to Problem 5
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Office hours
11am-12:30pm on Monday, by Zoom.
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Syllabus
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Slides (Feedback on typos appreciated)
- Combinatorial analysis
- Axioms of probability
- Conditional probability and independence
- Random variables
- Continuous random variables
- Jointly distributed random variables
- Limit theorems
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Documents with computations (notes from lectures)
- Lesson 1
- Lesson 2
- Lesson 3
- Lesson 4
- Lesson 5
- Lesson 6
- Lesson 7
- Lesson 8
- Lesson 9
- Lesson 10
- Lesson 11
- Lesson 12
- Lesson 13
- Lesson 14
- Lesson 15
- Lesson 17
- Lesson 18
- Lesson 19
- Lesson 20
- Lesson 21
- Lesson 22
- Lesson 23
- Lesson 24
- Lesson 25
- Lesson 26
- Lesson 27
- Lesson 28
- Lesson 29
- Lesson 30
- Lesson 33
- Lesson 34
- Lesson 35
- Lesson 36
- Lesson 37
- Lesson 38
- Lesson 39
- Lesson 40
- Lesson 41
- Lesson 42
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