This book is an outgrowth of our involvement in teaching an introductory probability course ("Probabiblistic Systems Analysis") at the Massachusetts Institute of Technology. The course is attended by a large number of students with diverse backgrounds, and a broad range of interests. They span the entire spectrum from freshmen to beginninge graduate students, and from the engineering school to the school of management. Accordingly, we have tried to strike a balance between simplicity in exposition and sophistication in analytical reasoning.
An edition of Introduction to Probability
(2008)
Introduction to Probability
Second Edition
by Dimitri P. Bertsekas and John N. Tsitsiklis
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An introduction to probability theory and probabilistic models used in science, engineering, economics and related fields.
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Introduction to Probability
2008, Athena Scientific
Hardcover
in English
- Second Edition
188652923X 9781886529236
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Book Details
Table of Contents
1. Sample Space and Probability.
1
1.1. Sets.
3
1.2. Probabilistic Models.
6
1.3. Conditional Probability.
18
1.4. Total Probability Theorem and Bayes' Rule.
28
1.5. Independence.
34
1.6. Counting.
44
1.7. Summary and Discussion.
51
Problems.
53
2. Discrecte Random Variables.
71
2.1. Basic Concepts.
72
2.2. Probability Mass Functions.
74
2.3. Functions of Random Variables.
80
2.4. Expectation, Mean and Variance.
81
2.5. Joint PMFs of Multiple Random Variables.
92
2.6. Conditioning.
97
2.7. Independence.
109
2.8. Summary and Discussion.
115
Problems.
119
3. General Random Variables.
139
3.1. Continuous Random Variables and PDFs.
140
3.2. Cumulative Distribution Functions.
148
3.3. Normal Random Variables.
153
3.4. Joint PDFs of Multiple Random Variables.
158
3.5. Conditioning.
164
3.6. The Continuous Bayes' Rule.
178
3.7. Summary and Discussion.
182
Problems.
184
4. Further Topics on Random Variables.
201
4.1. Derived Distributions.
202
4.2. Covariance and Correlation.
217
4.3. Conditional Expectation and Variance Revisited.
222
4.4. Transforms.
229
4.5. Sum of a Random Number of Independent Random Variables.
240
4.6. Summary and Discussion.
244
Problems.
246
5. Limit Theorems.
263
5.1. Markov and Chebyshev Inequalities.
265
5.2. The Weak Law of Large Numbers.
269
5.3. Convergence in Probability.
271
5.4. The Central Limit Theorem.
273
5.5. The Strong Law of Large Numbers.
280
5.6. Summary and Discussion.
282
Problems.
284
6. The Bernoulli and Poisson Processes.
295
6.1. The Bernoulli Process.
297
6.2. The Poisson Process.
309
6.3. Summary and Discussion.
324
Problems.
326
7. Markov Chains.
339
7.1. Discrete-Time Markov Chains.
340
7.2. Classification of States.
346
7.3. Steady-State Behavior.
352
7.4. Absorption Probabilities and Expected Time to Absorption.
362
7.5. Continous-Time Markov Chains.
369
7.6. Summary and Discussion.
378
Problems.
380
8. Bayesian Statistical Inference.
407
8.1. Bayesian Inference and the Posterior Distribution.
412
8.2. Point Estimation, Hypothesis Testing, and the MAP Rule.
420
8.3. Bayesian Least Mean Squares Estimation.
430
8.4. Bayesian Linear Least Mean Squares Estimation.
437
8.5. Summary and Discussion.
444
Problems.
446
9. Classical Statistical Inference.
459
9.1. Classical Parameter Estimation.
462
9.2. Linear Regression.
477
9.3. Binary Hypothesis Testing.
486
9.4. Significance Testing.
496
9.5. Summary and Discussion.
505
Problems.
507
Index.
521
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Excerpts
added by Andreas Perstinger.
Excerpt taken from the preface which describes the aim of the book.
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| July 1, 2019 | Edited by MARC Bot | import existing book |
| July 29, 2014 | Edited by ImportBot | import new book |
| March 6, 2011 | Edited by Andreas Perstinger | Details added |
| March 6, 2011 | Created by Andreas Perstinger | Added new book. |