Table of Contents:
Part I. Probability, Random Variables and Statistics:
1. Introduction;
2. Probability;
3. Discrete random variables;
4. Continuous random variables;
5. Functions of random variables and their distributions;
6. Fundamentals of statistical analysis;
7. Distributions derived from the normal distribution
Part II. Transform Methods, Bounds and Limits:
8. Moment-generating function and characteristic function;
9. Generating function and Laplace transform;
10. Inequalities, bounds and large deviation approximation;
11. Convergence of a sequence of random variables, and the limit theorems --
Part III. Random Processes:
12. Random process;
13. Spectral representation of random processes and time series;
14. Poisson process, birth-death process, and renewal process;
15. Discrete-time Markov chains;
16. Semi-Markov processes and continuous-time Markov chains;
17. Random walk, Brownian motion, diffusion and Itô processes --
Part IV. Statistical Inference:
18. Estimation and decision theory;
19. Estimation algorithms --
Part V. Applications and Advanced Topics:
20. Hidden Markov models and applications;
21. Probabilistic models in machine learning;
22. Filtering and prediction of random processes;
23. Queuing and loss models.

Summary:
Together with the fundamentals of probability, random processes and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric.