# Math 20: Probability

ORC Course Description: This course gives a foundational introduction to probability theory. Topics covered include (discrete and continuous) random variables, multivariate distributions, expectations, independence, conditioning, conditional distributions and expectations, law of large numbers and the central limit theorem, random walks, Markov chains and their applications.

Textbook: Introduction to Probability (2nd Rev Ed), Charles M. Grinstead & J. Laurie Snell, American Mathematical Society (1997). By courtesy of the authors, this book is freely available on the internet (here).

Grading Formula: Participation & in-class quizzes (10%) + Weekly homework problem sets (20%) + Midterm 1 (20%) + Midterm 2 (20%) + Final (30%).

• Instructor: Professor Feng Fu, Mathematics Department, Dartmouth College
• Course Time: MWF 11:30-12:35 (x-hour Tu 12:15-1:05) at 006 Kemeny Hall
• Office Hours: Mon 2:00pm-3:00pm, Wed 2:00pm-3pm, and by appointment.
• Office: 210 Kemeny Hall
• Email: feng.fu@dartmouth.edu

## Important Dates

• Homework due weekly on Friday
• Midterm 1: 24 July 2019, 6:30pm-8:30pm @ Kemeny Hall 006
• Midterm 2: 12 August 2019, 6:30pm-8:30pm @ Kemeny Hall 006
• Final Exam: Saturday, August 24, 2019 at 8:00am
31 July 2019: Final day to drop a 4th course;
7 August 2019: Final day to withdraw a course.

## Syllabus

Tentative lecture plan which may be subject to further changes.

Date Lecture Homework
21 June 2019 Course Overview & Basic Concepts of Discrete Probability Ch.1.2: 6, 7, 13, 14, 23
24 June 2019 Guest lecture by Xingru Chen: Continuous Probability Densities suggested reading: Ch. 2
26 June 2019 No class (makeup class on x-hr) suggested reading: Ch. 3
28 June 2019 No class (makeup class on x-hr) HW: Ch. 2.2: 6, 8(a),(b),(c),(d),(e),(h)
1 July 2019 Permutations Ch. 3.2: 7, 8, 9, 16, 22, 23, 32
2 July 2019 X-HR: Combinations Reading: Ch. 4.1 & 4.2
3 July 2019 Discrete Conditional Probability
5 July 2019 Continuous Conditional Probability Ch. 4.1: 14, 17, 26, 36; 4.2: 3, 5(c)(d)
8 July 2019 Important Distributions & Densities Ch. 5.1: 11, 32, 39; 5.2: 2, 10, 31, 34, 37
9 July 2019 X-HR: Expected Value & Variance Ch. 6.1 7, 13; 6.2: 15, 18, 20, 22, 27
10 July 2019 Expected Value & Variance of Continuous Random Variables Ch. 6.3: 3, 8, 10, 12, 17, 26, 28
12 July 2019 Sums of Independent Random Variables
15 July 2019 Review of Functions of Random Variables
17 July 2019 Weak Law of Large Numbers
19 July 2019 Generating Functions for Discrete Random Variables
22 July 2019 Generating Functions for Continuous Densities
24 July 2019 Midterm 1
26 July 2019 Central Limit Theorem
29 July 2019 Theory of Branching Processes I
31 July 2019 Theory of Branching Processes II
31 July 2019 Last day to drop a 4th class
2 August 2019 Markov Chains
5 August 2019 Fundamental Limit Theorem
7 August 2019 Mean First Passage Time
7 August 2019 Final day for withdrawing a course
9 August 2019 Markov Process in Continuous Time (Poisson Process)
12 August 2019 Random Walks
12 August 2019 Midterm 2
14 August 2019 Gambler’s Ruin
16 August 2019 Diffusion Limit of Random Walks
19 August 2019 Applications of Probability Theory
21 August 2019 Last day of class: Review of finals
24 August 2019 Final Exam at 8:00am

## Course Policies

### Honor Principle

Collaborations (giving and receiving assistance) during closed-book exams and quizzes are strictly prohibited. Any form of plagiarism is not allowed in the final project. If you have questions, please ask the instructor before doing and should always refer to Academic Honor Principle.

### Accessibility Policy

Students with disabilities who may need disability-related academic adjustments and services for this course are encouraged to see me privately as early in the term as possible. Students requiring disability-related academic adjustments and services must consult the Student Accessibility Services office (Carson Hall, Suite 125, 646-9900). Once SAS has authorized services, students must show the originally signed SAS Services and Consent Form and/or a letter on SAS letterhead to their professor. As a first step, if students have questions about whether they qualify to receive academic adjustments and services, they should contact the SAS office. All inquiries and discussions will remain confidential.

### Student Religious Observances

Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with the course instructor before the end of the second week of the term to discuss appropriate accommodations.

### Late Policy

By "deadline" we really mean it. On the condition of accepting the penalty for turning in the homework assignments late (that is, 5% each additional day), however, an extension of maximum 4 days will be granted on a case-by-case basis. In exceptional circumstances, students with disabilities should inform the instructor of their accommodation requests well in advance, so that the instructor will have sufficient time to work with Student Accessibility Services to provide appropriate accommodations.