# Math 3332: Probability Theory (Fall 2024)

## General Information

Instructor: Mikhail Lavrov
Location: Mathematics 116
Lecture times: 6:30pm to 7:45pm on Tuesday and Thursday
Textbook: Introduction to Probability, Statistics, and Random Processes by Hossein Pishro-Nik, available online at https://www.probabilitycourse.com/
Office hours: 12:00pm to 2:00pm on Wednesday..
D2L page: https://kennesaw.view.usg.edu/d2l/home/3287993.

D2L will be used to submit assignments (these will be posted both here and on D2L, for convenience) and to view grades. The syllabus will also be posted there.

During the scheduled office hours, you should feel free to show up with no notice if you have questions of any kind.

If it turns out you are not available during that time, begin by emailing me; if your questions are easy to answer by email, I will do that, and if not, we can find another time to meet. (Allow some time for me to check my email.)

## Homework and Exams

There will be eight homework assignments, two midterm exams, and one final exam; the dates are marked below.

I will post the homework assignments here and on D2L; they are always due on Friday at 11:59pm, via D2L.

Midterm exams will be given in person during our ordinary 75-minute class period.

## Detailed Schedule

A note in the format "PN 1.2.3" is a reference to section 1.2.3 of the official textbook (linked above). I strongly encourage reading the textbook to supplement lectures, and working through the many problems included in the textbook.

Section 11.2 of the textbook has some material on Markov chains, but I've also written my own notes on Markov chains to supplement it: markov-chains.pdf. The letters MC indicate references to this document.

• Date
Topic Covered
Other details
• Tue 8/13
Finding probabilities
PN 1.3.3
• Thu 8/15
Random experiments
PN 1.3.1-1.3.2
• Tue 8/20
Models of probability
PN 1.3.4-1.3.5
• Thu 8/22
Conditional probability
PN 1.4
HW 1 due Friday
• Tue 8/27
Law of total probability
PN 1.4.2
• Thu 8/29
Bayes' rule
PN 1.4.3
• Tue 9/3
Bayes' rule: fancier examples
PN 1.4.3
• Thu 9/5
Counting strategies
PN 2.1.0-2.1.2
HW 2 due Friday
• Tue 9/10
Binomial coefficients
PN 2.1.3-2.1.4
• Thu 9/12
Multinomials and multisets
PN 2.1.4
• Tue 9/17
Random variables
PN 3.1
• Thu 9/19
Intro to Markov chains
PN 11.2.1-11.2.3, MC Section 1
HW 3 due Friday
• Tue 9/24
Stationary distributions
PN 11.2.4, 11.2.6, MC Section 2
• Thu 9/26
Exam 1

• Tue 10/1
Expected values
PN 3.2.2
• Thu 10/3
Special distributions
PN 3.1.5
HW 4 due Friday
• Tue 10/8
Transformations
PN 3.2.3
• Thu 10/10
Conditional distributions
PN 5.1.3, 5.1.5
• Tue 10/15
Markov chain hitting times
PN 11.2.5, MC Section 3
• Thu 10/17
Variance
PN 3.2.4
HW 5 due Friday
• Tue 10/22
Sums of random variables
PN 5.3.1, 6.1.2
• Thu 10/24
Joint distributions
PN 5.1.1, 5.1.4
HW 6 due Friday
• Tue 10/29
(Flex time for previous topics)

• Thu 10/31
Exam 2

• Tue 11/5
Continuous random variables
PN 4.1.0, 4.2.1, 4.2.2
• Thu 11/7
Probability densities
PN 4.1.1, 4.2.1, 4.2.2
HW 7 due Friday
• Tue 11/12
Expected values
PN 4.1.2, 4.2.3
• Thu 11/14
Transformations
PN 4.1.3, 5.2.3
• Tue 11/19
Mixed random variables
PN 4.3.1-4.3.2
• Thu 11/21
Poisson processes
PN 4.2.4, 11.1
HW 8 due Friday
• Thu 12/5
Final exam (6:00pm - 8:00pm)