Textbook in PDF format

Preface
Notations and Abbreviations
Permutation and Combination
Introduction
Permutations
Combinations
Basic Principles of Counting
Binomial and Multinomial Coefficients
Occupancy Problems
Combinatorial Generating Functions
Exploring with Mathematica
Problems
Remarks and References
Axioms of Probability
Introduction
Sample Space, Events, and Sets
Axioms of Probability
Sample Space Having Equally Likely Outcomes
The Importance of Being Truly Random
Probability as a Continuous Set Function
The Subjective Probability
Exploring with Mathematica
Problems
Remarks and References
Conditional Probability
Introduction
Conditional Probabilities and Independence
The Law of Total Probabilities
Bayes Theorem
Artificial Intelligence and Bayes Theorem
More on Problem Solving by Conditioning
Exploring with Mathematica
Problems
Remarks and References
Random Variables
Introduction
Distribution Functions
Functions of a Random Variable
Expectation of a Random Variable
Random Variables that are Neither Discrete nor Continuous
Various Transforms for Applications in Probability
Higher Moments of a Random Variable
Exploring with Mathematica
Problems
Remarks and References
Discrete Random Variab
Introduction
Bernoulli and Binomial Random Variables
Hypergeometric Random Variables
Poisson Random Variables
Geometric and Negative Binomial Random Variables
Probability Generating Functions
Summary
Exploring with Mathematica
Problems
Remarks and References
Continuous Random Variables
Introduction and Transformation of Random Variables
Laplace Transforms and Characteristic Functions
Uniform and Exponential Random Variable
Erlang and Gamma Random Variables
Weibull Random Variables
Normal and Lognormal Random Variables
More Continuous Random Variables and Variance Gamma
Summary
Exploring with Mathematica
Problems
Remarks and References
Jointly Distributed Random Variables
Introduction and Distribution Functions
Independent Random Variables
Order Statistics
Conditional Random Variables
Functions of Jointly Distributed Random Variables
More Well-Known Distributions
Mixtures of Random Variables
Exploring with Mathematica
Problems
Remarks and References
Dependence and More on Expectations
Introduction
Exchangeable Random Variables
Dependence
Bivariate Normal Distributions
More on Expectations and Related Subjects
Sampling from a Finite Population
Exploring with Mathematica
Problems
Remarks and References
Limit Theorems
Markov and Chebyshev’s Inequalities
Various Forms of Convergence
Characteristics Functions
Weak Law of and Strong Law of Large Numbers
Central Limit Theorem
Other Inequalities
Exploring with Mathematica
Problems
Remarks and References
A Terse Introduction to Mathematica
Four Simple Examples
Answers to Odd-Numbered Problems