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Introduction to Probability (2E) by Dimitri Bertsekas, John Tsitsiklis
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About this book :-
Introduction to Probability (2E) written by Dimitri Bertsekas, John Tsitsiklis
This text introduction to probability theory, stochastic processes, and probabilistic models used in science, engineering, economics, and related fields. The book is the currently used textbook for "Probabilistic Systems Analysis" an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students. 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, as well as the fundamental concepts and methods of statistical inference, both Bayesian and classical. 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. 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.
Book Detail :-
Title: Introduction to Probability (2E)
Edition: Second Edition
Author(s): Dimitri Bertsekas, John Tsitsiklis
Publisher: Athena Scientific
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About Author :-
The author Dimitri Panteli Bertsekas (born 1942, Athens) is an applied mathematician, electrical engineer, and computer scientist, a McAfee Professor at the Department of Electrical Engineering and Computer Science in School of Engineering at the Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts, and also a Fulton Professor of Computational Decision Making at Arizona State University, Tempe.
Bertsekas studied for five years at the National Technical University of Athens, Greece and studied for about a year and a half at The George Washington University, Washington, D.C., where he obtained his M.S. in electrical engineering in 1969, and for about two years at MIT, where he obtained his doctorate in system science in 1971. Prior to joining the MIT faculty in 1979, he taught for three years at the Engineering-Economic Systems Dept. of Stanford University, and for five years at the Electrical and Computer Engineering Dept. of the University of Illinois at Urbana-Champaign. In 2019, he was appointed a full-time professor at the School of Computing and Augmented Intelligence at Arizona State University, Tempe, while maintaining a research position at MIT.
He is known for his research work, and for his nineteen textbooks and monographs in theoretical and algorithmic optimization and control, in reinforcement learning, and in applied probability.
The author John N. Tsitsiklis (born 1958) is a Professor of Electrical Engineering with the Department of Electrical Engineering and Computer Science (EECS) at the Massachusetts Institute of Technology. He received a B.S. degree in Mathematics (1980), and his B.S. (1980), M.S. (1981), and Ph.D. (1984) degrees in Electrical Engineering, all from the Massachusetts Institute of Technology in Cambridge, Massachusetts.
He serves as the director of the Laboratory for Information and Decision Systems and is affiliated with the Institute for Data, Systems, and Society (IDSS), the Statistics and Data Science Center and the MIT Operations Research Center.
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Book Contents :-
Introduction to Probability (2E) written by
Dimitri Bertsekas, John Tsitsiklis
cover the following topics.
1. Sample Space and Probability
1.2. Probabilistic Models
1.3. Conditional Probability
1.4. Total Probability Theorem and Bayes' Rule
2. Discrete Random Variables
2.1. Basic Concepts
2.2. Probability Mass Functions
2.3. Functions of Random Variables
2.4. Expectation, Mean, and Variance
2.5. Joint PMFs of ?lultiple Random Variables
3. General Random Variables
3.1. Continuous Random Variables and PDFs
3.2. Cumulative Distribution Functions
3.3. Normal Random Variables
3.4. Joint PDFs of Multiple Random Variables
3.6. The Continuous Bayes' Rule
4. Further Topics on Random Variables
4.1. Derived Distributions
4.2. Covariance and Correlation
4.3. Conditional Expectation and Variance Revisited
4.5. Sum of a Random Number of Independent Random Variables
5. Limit Theorems
5.1. Markov and Chebyshev Inequalities
5.2. The Weak Law of Large Numbers
5.3. Convergence in Probability
5.4. The Central Limit Theorem
5.5. The Strong Law of Large Numbers
6. The Bernoulli and Poisson Processes
6.1. The Bernoulli Process
6.2. The Poisson Process
7. Markov Chains
7.1. Discrete-Time Markov Chains
7.2. Classification of States
7.3. Steady-State Behavior
7.4. Absorption Probabilities and Expected Time to Absorption
7.5. Continuous-Time Markov Chains
8. Bayesian Statistical Inference
8.1. Bayesian Inference and the Posterior Distribution
8.2. Point Estimation, Hypothesis Testing, and the MAP Rule
8.3. Bayesian Least Mean Squares Estimation
8.4. Bayesian Linear Least Mean Squares Estimation
9. Classical Statistical Inference
9.1. Classical Parameter Estimation
9.2. Linear Regression
9.3. Binary Hypothesis Testing
9.4. Significance Testing
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