ISBN13: 978-1886529403

ISBN10: 188652940X

Cover type:

Edition/Copyright: 02

Publisher: Athena Scientific

Published: 2002

International: No

ISBN10: 188652940X

Cover type:

Edition/Copyright: 02

Publisher: Athena Scientific

Published: 2002

International: No

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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**

**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

Dimitri P. Bertsekas and John N. Tsitsiklis

ISBN13: 978-1886529403ISBN10: 188652940X

Cover type:

Edition/Copyright: 02

Publisher: Athena Scientific

Published: 2002

International: No

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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