# Probability and Stochastic Processes, 3ed, An Indian Adaptation

ISBN: 9789354243455

492 pages

## Description

Probability and Stochastic Processes – A Friendly Introduction for Electrical and Computer Engineers, Third Edition is an extensive discourse that introduces engineering students to probability theory and stochastic processes. The book presents intuitive explanations of key points in order to help students apply math to practical engineering problems.

Preface to the Indian Adaptation

Preface to the US Edition

Reviewers Panel

1 Random Experiments, Models, and Probabilities

1.1 Applying Set Theory to Probability

1.2 Probability Axioms

1.3 Conditional Probability

1.4 Partitions and the Law of Total Probability

1.5 Bayes’ Theorem

1.6 Independence

1.7 Matlab

2 Sequential Random Experiments

2.1 Tree Diagrams

2.2 Counting Methods

2.3 Independent Trials

2.4 Matlab

3 Discrete Random Variables

3.1 Definitions

3.2 Probability Mass Function

3.3 Families of Discrete Random Variables

3.4 Cumulative Distribution Function (CDF)

3.5 Averages and Expected Value

3.6 Functions of a Random Variable

3.7 Expected Value of a Derived Random Variable

3.8 Variance and Standard Deviation

3.9 Matlab

4 Continuous Random Variables

4.1 Continuous Sample Space

4.2 The Cumulative Distribution Function

4.3 Probability Density Function

4.4 Expected Values

4.5 Families of Continuous Random Variables

4.6 Gaussian Random Variables

4.7 Delta Functions, Mixed Random Variables

4.8 Matlab

5 Multiple Random Variables

5.1 Joint Cumulative Distribution Function

5.2 Joint Probability Mass Function

5.3 Marginal PMF

5.4 Joint Probability Density Function

5.5 Marginal PDF

5.6 Independent Random Variables

5.7 Expected Value of a Function of Two Random Variables

5.8 Covariance, Correlation and Independence

5.9 Bivariate Gaussian Random Variables

5.10 Multivariate Probability Models

5.11 Matlab

6 Probability Models of Derived Random Variables

6.1 PMF of a Function of Two Discrete Random Variables

6.2 Functions Yielding Continuous Random Variables

6.3 Functions Yielding Discrete or Mixed Random Variables

6.4 Continuous Functions of Two Continuous Random Variables

6.5 PDF of the Sum of Two Random Variables

6.6 Matlab

7 Conditional Probability Models

7.1 Conditioning a Random Variable by an Event

7.2 Conditional Expected Value Given an Event

7.3 Conditioning Two Random Variables by an Event

7.4 Conditioning by a Random Variable

7.5 Conditional Expected Value Given a Random Variable

7.6 Bivariate Gaussian Random Variables: Conditional PDFs

7.7 Matlab

8 Random Vectors

8.1 Vector Notation

8.2 Independent Random Variables and Random Vectors

8.3 Functions of Random Vectors

8.4 Expected Value Vector and Correlation Matrix

8.5 Gaussian Random Vectors

8.6 Matlab

9 Sums of Random Variables

9.1 Expected Values of Sums

9.2 Moment Generating Functions

9.3 MGF of the Sum of Independent Random Variables

9.4 Characteristic Function and Probability Generating Function

9.5 Matlab

10 Some Probabilistic Inequalities and Bounds

10.1 Markov Inequality

10.2 Chebyshev’s Inequality

10.3 Chernoff Bound

10.4 Central Limit Theorem

10.5 Sample Mean and Variance

10.6 Laws of Large Numbers (LLN)

11 Stochastic Processes and Markov Chains

11.1 Definitions and Examples

11.2 Random Variables from Random Processes

11.3 Independent, Identically Distributed Random Sequences

11.4 The Poisson Process

11.5 Properties of the Poisson Process

11.6 The Brownian Motion Process

11.7 Markov Process

11.8 Discrete-Time Markov Chains

11.9 Higher Transition Probabilities: Chapman–Kolmogorov Equations

11.10 Long-Run Behavior of Markov Chains

11.11 Classification of States of Chains

11.12 Markov Chains with Countably Infinite States

11.13 Ergodic and Reducible Chains

11.14 Birth Process and Death Process

11.15 Queuing Models – Poisson Queues

11.16 Matlab

12 Stationary Processes and Random Signal Processing

12.1 Expected Value and Correlation

12.2 Stationary Processes

12.3 Wide Sense Stationary Processes

12.4 Cross-Correlation

12.5 Gaussian Processes

12.6 Linear Filtering of Continuous-Time Stochastic Processes

12.7 Linear Filtering of a Random Sequence

12.8 Discrete-Time Linear Filtering: Vectors and Matrices

12.9 Power Spectral Density of a Continuous-Time Process

12.10 Power Spectral Density of a Random Sequence

12.11 Cross Power Spectral Density

12.12 Frequency Domain Filter Relationships

12.13 Matlab

Problems

Appendix A Families of Random Variables

A.1 Discrete Random Variables

A.2 Continuous Random Variables

Appendix B A Few Math Facts

References

Index