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