Math 3332: Probability and Inference (Spring 2021)

General Information

Instructor: Mikhail Lavrov
Location: Mathematics Building 237.
Lecture times: 11:15am-12:05pm on Monday if your last name begins A-L and on Wednesday if your last name begins M-Z.
Textbook: Introduction to Probability, Statistics, and Random Processes by Hossein Pishro-Nik, available online at https://www.probabilitycourse.com/.
Office hours: Wednesday 10am-11am and Friday 11am-12pm, online via Collaborate Ultra.
D2L page: https://kennesaw.view.usg.edu/d2l/home/2199846.

More information is available on D2L, where I will post the syllabus, homework assignments and solutions, exams, and more. This webpage is primarily for posting recorded lectures.

Homework and Exams

There will be eight homework assignments, two midterm exams, and one final exam. The dates are marked below, but you can find and submit the assignments on D2L. No part of your grade will depend on coming to class.

Detailed Schedule

The textbook sections listed below are a good source for what we'll talk about on each day, but we won't always cover everything the textbook covers, or do things in the same order. I am not going to expect you to learn material from the textbook that I don't cover in lectures.

If you are interested in my slides, here are the links. I don't think that reading the slides is a good replacement for watching the lecture videos or attending class.

• Slides on random experiments (January 11th to February 17th)
• Slides on discrete random variables (February 22nd to March 31st)
• Slides on continuous random variables (April 2nd to May 3rd)

My goal is to have all the recordings for each week posted by the beginning of that week.

• Date
  Textbook
  Recordings
  Assignments
• Mon 1/11
  1.2 Review of Set Theory
  • Hello!
  • Kinds of sets
  • Set operations
   
• Wed 1/13
  1.3.2 Probability
  • What is probability?
  • Probability axioms
   
• Fri 1/15
  1.3.3 Finding Probabilities
  • Basic strategies
  • Fancier methods
   
• Mon 1/18
  No Class
   
   
• Wed 1/20
  1.3.4 Discrete Models
  • About week 2
  • Finite spaces
  • Infinite models
   
• Fri 1/22
  1.3.5 Continuous Models
  • Continuous models
  • Uncountability
  HW 1 due
• Mon 1/25
  1.4 Conditional Probability
  • About week 3
  • Cond. probability
  • The chain rule
   
• Wed 1/27
  1.4.1 Independence
  • Two indpnt. events
  • Many events
   
• Fri 1/29
  1.4.2 Law of Total Probability
  • Law of total prob.
  • Examples
   
• Mon 2/1
  1.4.3 Bayes' Rule
  • About week 4
  • Bayes' rule
  • Odds calculations
   
• Wed 2/3
  11.2 Discrete-Time Markov Chains
  • Markov chains
  • Examples
   
• Fri 2/5
  Probability Paradoxes
  • Monty Hall
  • Two girls problem
  HW 2 due
• Mon 2/8
  2.1 Combinatorics
  • About week 5
  • Multiplication
  • Overcounting
   
• Wed 2/10
  2.1.1-2 Ordered Sampling
  • ...with replacement
  • ...w/o replacement
   
• Fri 2/12
  2.1.3 Unordered without Replacement
  • Combinations
  • Binomial formula
  HW 3 due
• Mon 2/15
  2.1.4 Unordered with Replacement
  • About week 6
  • Multinomials
  • Counting multisets
   
• Wed 2/17
  Counting review
  • Marbles in a bag
  • Disjoint subsets
  • Binomial problems
   
• Fri 2/19
  Exam 1 (due at 11:59pm)
   
   
• Mon 2/22
  3.1 Random Variables
  • About week 7
  • Definitions
  • Examples
   
• Wed 2/24
  3.1.5 Special Distributions
  • Binomial
  • Geometric
   
• Fri 2/26
  3.2.2 Expectation
  • Expected value
  • Computations
   
• Mon 3/1
  3.1.5 Special Distributions
  • About week 8
  • Pascal distribution
  • Hypergeometric
  • Poisson distribution
  HW 4 due
• Wed 3/3
  3.2.3 Functions of Random Variables
  • The PMF of g(X)
  • E[g(X)] and LOTUS
   
• Fri 3/5
  3.2.4 Variance
  • What is variance?
  • How to interpret it
   
• 3/8-3/14
  Spring Break: No Class
   
   
• Mon 3/15
  3.1.4 Independent Random Variables
  • About week 9
  • Covariance
  • Independence
   
• Wed 3/17
  More Variance Calculations
  • Variance of a sum
  • Var of Hyper(b,r,k)
   
• Fri 3/19
  6.1.3 Moment Generating Functions
  • Properties of PGFs
  • Finding moments
  HW 5 due
• Mon 3/22
  6.2 Probability Bounds
  • About week 10
  • Chernoff bounds
  • Laws of large nos.
   
• Wed 3/24
  5.1 Two Discrete Random Variables
  • Joint distributions
  • Functions of 2 vars.
   
• Fri 3/26
  5.1.3 Conditioning and Independence
  • 1 random variable
  • 2 random variables
   
• Mon 3/29
  5.1.5 Conditional expectation
  • About week 11
  • Cond. expectation
  • What is E[X|Y]?
   
• Wed 3/31
  9.1.1 Prior and Posterior
  • Bayes' rule, again
  • Another example
   
• Fri 4/2
  4.1 Continuous Random Variables
  • CDFs
  • Examples of CDFs
  HW 6 due
• Mon 4/5
  4.1.1 Probability Density Function
  • About week 12
  • PDFs
  • Examples of PDFs
   
• Wed 4/7
  4.2.2 Exponential Distribution
  • Radioactive decay
  • The exponential
   
• Fri 4/9
  Exam 2 (due at 11:59pm)
   
   
• Mon 4/12
  4.1.2 Expected Value and Variance
  • About week 13
  • Expected value
  • Examples
   
• Wed 4/14
  4.1.3 Functions of Random Variables
  • Transforming CDFs
  • Transforming PDFs
   
• Fri 4/16
  4.2.3 Normal Distribution
  • Normal distribution
  • Approximations
   
• Mon 4/19
  11.1 Poisson processes
  • About week 14
  • Poisson processes
  • Gamma distribution
  • Merging/splitting
  HW 7 due
• Wed 4/21
  5.2 Two Continuous Random Variables
  • Joint PDFs
  • Functions of 2 vars.
   
• Fri 4/23
  5.2.3 Conditioning and Independence
  • 1-variable case
  • 2-variable case
   
• Mon 4/26
  Mixture Distributions
  • About week 15
  • Mixtures
  • Mixture examples
   
• Wed 4/28
  4.3 Mixed Random Variables
  • CDFs of mixed r.v.s
  • The delta function
   
• Fri 4/30
  8.4 Hypothesis Testing
  • NHST framework
  • Examples
  HW 8 due
• Mon 5/3
  9.1 Bayesian Inference
  • Coin-flipping
  • The posterior
  • Thank you
   
• Wed 5/5
  Final Exam (due 5/6 at 11:59pm)