# Free Textbook: Probability Course, Harvard University (Based on R)

Free Textbook: Probability Course, Harvard University (Based on R)

A free online version of the second edition of the book based on Stat 110, Introduction to Probability by Joe Blitzstein and Jessica Hwang, is now available here. Print copies are available via CRC Press, Amazon, and elsewhere.  Stat110x is also available as an free edX course, here.
The edX course focuses on animations, interactive features, readings, and problem-solving, and is complementary to the Stat 110 lecture videos on YouTube, which are available here. The Stat110x animations are available within the course and here. For more information, visit Stat110 at Harvard. A 10-page cheat sheet summarizing the content, is available here. For more free books, visit this page.

1. Probability and Counting

Why study probability?
Sample spaces and Pebble World
Naive definition of probability
How to count
Story proofs
Non-naive definition of probability
Recap
R
Exercises

2. Conditional Probability

The importance of thinking conditionally
Definition and intuition
Bayes’ rule and the law of total probability
Conditional probabilities are probabilities
Independence of events
Coherency of Bayes’ rule
Conditioning as a problem-solving tool
Recap
R
Exercises

3. Random Variables and Their Distributions

Random variables
Distributions and probability mass functions
Bernoulli and Binomial
Hypergeometric
Discrete Uniform
Cumulative distribution functions
Functions of random variables
Independence of rvs
Connections between Binomial and Hypergeometric
Recap
R
Exercises

4. Expectation

Definition of expectation
Linearity of expectation
Geometric and Negative Binomial
Indicator rvs and the fundamental bridge
Law of the unconscious statistician (LOTUS)
Variance
Poisson
Connections between Poisson and Binomial
*Using probability and expectation to prove existence
Recap
R
Exercises

5. Continuous Random Variables

Probability density functions
Uniform
Universality of the Uniform
Normal
Exponential
Poisson processes
Symmetry of iid continuous rvs
Recap
R
Exercises

6. Moments

Summaries of a distribution
Interpreting moments
Sample moments
Moment generating functions
Generating moments with MGFs
Sums of independent rvs via MGFs
*Probability generating functions
Recap
R
Exercises

7. Joint Distributions

Joint, marginal, and conditional
D LOTUS
Covariance and correlation
Multinomial
Multivariate Normal
Recap
R
Exercises

8. Transformations

Change of variables
Convolutions
Beta
Gamma
Beta-Gamma connections
Order statistics
Recap
R
Exercises

9. Conditional Expectation

Conditional expectation given an event
Conditional expectation given an rv
Properties of conditional expectation
*Geometric interpretation of conditional expectation
Conditional variance
Recap
R
Exercises

10. Inequalities and Limit Theorems
Inequalities
Law of large numbers
Central limit theorem
Chi-Square and Student-t
Recap
R
Exercises
11. Markov Chains

Markov property and transition matrix
Classification of states
Stationary distribution
Reversibility
Recap
R
Exercises

12. Markov Chain Monte Carlo

Metropolis-Hastings
Recap
R
Exercises

13. Poisson Processes

Poisson processes in one dimension
Conditioning, superposition, thinning
Poisson processes in multiple dimensions
Recap
R
Exercises

A Math

Sets
Functions
Matrices
Difference equations
Differential equations
Partial derivatives
Multiple integrals
Sums
Pattern recognition

B R Programming

Vectors
Matrices
Math
Sampling and simulation
Plotting
Programming
Summary statistics
Distributions

C Table of distributions
Bibliography
Index

Link: Free Textbook: Probability Course, Harvard University (Based on R)