Probability Theory

Probability Theory Class Notes

Keywords: probability theory notes, Blitzstein and Hwang, sample spaces, counting, conditional probability, Bayes rule, random variables, expectation, variance, conditional expectation, central limit theorem.

As an instructor of introduction to probability theory, I prepared these PDFs as a review of the chapters in Introduction to Probability by Blitzstein and Hwang. They include example problems which have been worked out in some detail. I hope you find these useful.

Class Notes	In-Class Activities	Solutions
1.1 thru 1.4 Sample Space, Naive Definition, Counting, Over Counting	Activity 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 NonNaive	Activity 1.6	Solutions 1.6
2.1 Think Conditionally	Activity 2.1	Solutions 2.1
2.2 2.3 2.4 Conditional Probability, Bayes, LOTP	Activity 2.3	Solutions 2.3
2.5 2.8 Independence, Coherency, Problem Solving, Pitfalls and Paradoxes	Activity 2.5	Solutions 2.5
3.1 3.2 Random Variables, Distributions, Probability Mass Functions	—	—
3.3 3.5 Bernoulli, Binomial, Hypergeometric, Uniform	Activity 3.3–3.5	Solutions 3.3–3.5
3.6 3.8 Cumulative Distribution Functions, Functions of RVs, Independence	Activity 3.2, 3.6, 3.8	Solutions 3.2, 3.6, 3.8
4.1 4.3 Expectation, Linearity, Geometric, Negative Binomial	Activity 4.1, 4.5	Solutions 4.1, 4.5
4.5 4.6 LOTUS, Variance	Activity 4.6	Solutions 4.6
4.7 5.1 Poisson, Probability Density Functions	Activity 5.1	Solutions 5.1
5.2 5.3 Uniform, Universality	—	—
5.4 5.5 Normal, Exponential	Activity 5.4–5.5	Solutions 5.4–5.5
6.1 6.3 Distribution Summaries, Moments, Sample Moments	Activity 6.1–6.2	Solutions 6.1–6.2
6.4 Moment Generating Functions	Activity 6.2–6.4	Solutions 6.2–6.4
7.1 7.2 Joint Marginal, Conditional, 2D LOTUS	Activity 7.1 Activity 7.1 Activity 7.1, 7.2, 9.2	Solutions 7.1 Solutions 7.1 Solutions 7.1, 7.2, 9.2
8.1 Change of Variables	—	—
9.1 9.2 Conditional Expectation	—	—
7.3 Covariance Correlation	Activity 7.3	Solutions 7.3
10.1 10.2 Inequalities, Law of Large Numbers	—	—
10.3 Central Limit Theorem	Activity 9.3–9.6 Activity 10.3	Solutions 9.3–9.6 Solutions 10.3