Free Probability Theory Notes, Activities, and Solutions

Teaching

I have a license to teach mathematics at the secondary level in the state of Minnesota.

Minnesota State Teaching License

As an instructor of probability theory, I prepared these class notes as a review of the chapters in Introduction to Probability by Blitzstein and Hwang . These materials include notes, worked examples, in-class activities, and solutions.

Use the sections below to find materials by topic. Each unit can be expanded or collapsed to make the page easier to browse.

Counting, Sample Spaces, and the Foundations of Probability

Sample spaces, naive probability, counting, overcounting, stories, and non-naive probability.

Class NotesIn-Class ActivitiesSolutions
1.1 thru 1.4 Sample Space, Naive Definition, Counting, Over CountingActivity 1.1-1.4
Activity 1.1-1.2
Activity 1.4		Solutions 1.1-1.4
Solutions 1.1-1.2
Solutions 1.4
1.5 1.6 Stories NonNaiveActivity 1.6Solutions 1.6
Conditional Probability, Bayes' Theorem, and Independence

Conditional probability, Bayes' theorem, the Law of Total Probability, independence, coherency, and common probability pitfalls.

Class NotesIn-Class ActivitiesSolutions
2.1 Think ConditionallyActivity 2.1Solutions 2.1
2.2 2.3 2.4 Conditional Probability, Bayes, LOTPActivity 2.3Solutions 2.3
2.5 2.8 Independence, Coherency, Problem Solving, Pitfalls and ParadoxesActivity 2.5Solutions 2.5
Random Variables and Discrete Distributions

Random variables, probability mass functions, Bernoulli, binomial, hypergeometric, uniform, geometric, negative binomial, and Poisson distributions.

Class NotesIn-Class ActivitiesSolutions
3.1 3.2 Random Variables, Distributions, Probability Mass Functions——
3.3 3.5 Bernoulli, Binomial, Hypergeometric, UniformActivity 3.3-3.5Solutions 3.3-3.5
4.1 thru 4.3 Expectation, Linearity, Geometric, Negative Binomial——
4.7 5.1 Poisson, Probability Density FunctionsActivity 5.1Solutions 5.1
CDFs, Functions of Random Variables, and Independence

Cumulative distribution functions, functions of random variables, and independence.

Class NotesIn-Class ActivitiesSolutions
3.6 3.8 Cumulative Distribution Functions, Functions Of RVs, IndependenceActivity 3.2, 3.6, 3.8Solutions 3.2, 3.6, 3.8
Expectation, Variance, and Moments

Expectation, linearity, LOTUS, variance, moments, sample moments, and moment generating functions.

Class NotesIn-Class ActivitiesSolutions
4.5 4.6 LOTUS, VarianceActivity 4.1, 4.5
Activity 4.6		Solutions 4.1, 4.5
Solutions 4.6
6.1 6.3 Distribution Summaries, Moments, Sample MomentsActivity 6.1-6.2Solutions 6.1-6.2
6.4 Moment Generating FunctionsActivity 6.2-6.4Solutions 6.2-6.4
Continuous Distributions

Probability density functions, uniform distributions, universality, normal distributions, and exponential distributions.

Class NotesIn-Class ActivitiesSolutions
5.2 5.3 Uniform, Universality——
5.4 5.5 Normal, ExponentialActivity 5.4-5.5Solutions 5.4-5.5
Joint Distributions, Conditional Expectation, Covariance, and Correlation

Joint, marginal, and conditional distributions; two-dimensional LOTUS; conditional expectation; covariance; and correlation.

Class NotesIn-Class ActivitiesSolutions
7.1 7.2 Joint Marginal, Conditional, 2D LOTUSActivity 7.1
Activity 7.1b		Solutions 7.1
Solutions 7.1b
9.1 9.2 Conditional ExpectationActivity 7.1, 7.2, 9.2Solutions 7.1, 7.2, 9.2
7.3 Covariance CorrelationActivity 7.3Solutions 7.3
Change of Variables

Change-of-variables techniques for probability distributions.

Class NotesIn-Class ActivitiesSolutions
8.1 Change of Variables——
Limit Theorems

Inequalities, the Law of Large Numbers, and the Central Limit Theorem.

Class NotesIn-Class ActivitiesSolutions
10.1 10.2 Inequalities, Law Of Large Numbers——
10.3 Central Limit TheoremActivity 9.3-9.6
Activity 10.3		Solutions 9.3-9.6
Solutions 10.3