The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains, a number of more advanced topics, from which an instructor can choose to match the goals of a particular course. These topics include transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics.
The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis has been just intuitively explained in the text, but is developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems.
- Probability and Counting.
- Conditional Probability.
- Random Variables and Their Distributions.
- Continuous Random Variables.
- Joint Distributions.
- Conditional Expectation.
- Inequalities and Limit Theorems.
- Markov Chains.
- Markov Chain Monte Carlo.
- Poisson Processes.
Dimitri P. Bertsekas / John N. Tsitsiklis
188652923X | 978-1886529236