Introduction to Probability, Statistics, and Random Processes (Hossein Pishro-Nik)

Chapters 1 and 2: basic concepts such as random experiments, probability axioms, conditional probability, law of total probability, Bayes' rule, and counting methods;

Chapters 3 through 6: single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristics functions, random vectors, and inequalities;

Chapter 7: limit theorems and convergence;

Chapters 8 and 9: Bayesian and classical statistics;

Chapters 10: Introduction to random processes, processing of random signals;

Chapter 11: Poisson processes, discrete-time Markov chains, continuous-time Markov chains, and Brownian motion;

Chapter 12: basic methods of generating random variables and simulating probabilistic systems (using MATLAB);

Chapter 13: basic methods of generating random variables and simulating probabilistic systems (using R);

Chapter 14: recursive methods;