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Introduction to Probability

Introduction to Probability - 02 edition

ISBN13: 978-1886529403

Cover of Introduction to Probability 02 (ISBN 978-1886529403)
ISBN13: 978-1886529403
ISBN10: 188652940X
Cover type:
Edition/Copyright: 02
Publisher: Athena Scientific
Published: 2002
International: No

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Introduction to Probability - 02 edition

ISBN13: 978-1886529403

Dimitri P. Bertsekas and John N. Tsitsiklis

ISBN13: 978-1886529403
ISBN10: 188652940X
Cover type:
Edition/Copyright: 02
Publisher: Athena Scientific

Published: 2002
International: No
Summary

An intuitive, yet precise introduction to probability theory, stochastic processes, and probabilistic models used in science, engineering, economics, and related fields. This 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. 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, least squares estimation, the bivariate normal distribution, and 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.

Author Bio

Bertsekas, Dimitri P. : Massacussetts Institute of Technology

Tsitsiklis, John N. : Massachusetts Institute of Technology

Table of Contents

Sample Space and Probability

Sets
Probabilistic Models
Conditional Probability
Total Probability Theorem and Bayes' Rule
Independence
Counting
Summary and Discussion
Problems

Discrete Random Variables

Basic Concepts
Probability Mass Functions
Functions of Random Variables
Expectation, Mean, and Variance
Joint PMFs of Multiple Random Variables
Conditioning
Independence
Summary and Discussion
Problems

General Random Variables

Continuous Random Variables and PDFs
Cumulative Distribution Functions
Normal Random Variables
Conditioning on an Event
Multiple Continuous Random Variables
Derived Distributions
Summary and Discussion
Problems

Further Topics on Random Variables

Transforms
Sums of Independent Random Variables - Convolution
More on Conditional Expectation and Variance
Sum of a Random Number of Independent Random Variables
Covariance and Correlation
Least Squares Estimation
The Bivariate Normal Distribution
Summary and Discussion
Problems

Stochastic Processes

The Bernoulli Process
The Poisson Process
Summary and Discussion
Problems

Markov Chains

Discrete-Time Markov Chains
Classification of States
Steady-State Behavior
Absorption Probabilities and Expected Time to Absorption
Continuous-Time Markov Chains
Summary and Discussion
Problems

Limit Theorems

Markov and Chebyshev Inequalities
The Weak Law of Large Numbers
Convergence in Probability
The Central Limit Theorem
The Strong Law of Large Numbers
Summary and Discussion
Problems

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Cover of Introduction to Probability 2nd edition

Introduction to Probability - 2nd edition

ISBN13: 978-1886529236
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