Front Cover -- Fundamentals of Applied Probability and Random Processes -- Copyright Page -- Table of Contents -- Preface -- Acknowledgment -- Chapter 1. Basic Probability Concepts -- 1.1 Introduction -- 1.2 Sample Space and Events -- 1.3 Definitions of Probability -- 1.4 Applications of Probability -- 1.5 Elementary Set Theory -- 1.6 Properties of Probability -- 1.7 Conditional Probability -- 1.8 Independent Events -- 1.9 Combined Experiments -- 1.10 Basic Combinatorial Analysis -- 1.11 Reliability Applications -- 1.12 Chapter Summary -- 1.13 Problems -- 1.14 References -- Chapter 2. Random Variables -- 2.1 Introduction -- 2.2 Definition of a Random Variable -- 2.3 Events Defined by Random Variables -- 2.4 Distribution Functions -- 2.5 Discrete Random Variables -- 2.6 Continuous Random Variables -- 2.7 Chapter Summary -- 2.8 Problems -- Chapter 3. Moments of Random Variables -- 3.1 Introduction -- 3.2 Expectation -- 3.3 Expectation of Nonnegative Random Variables -- 3.4 Moments of Random Variables and the Variance -- 3.5 Conditional Expectations -- 3.6 The Chebyshev Inequality -- 3.7 The Markov Inequality -- 3.8 Chapter Summary -- 3.9 Problems -- Chapter 4. Special Probability Distributions -- 4.1 Introduction -- 4.2 The Bernoulli Trial and Bernoulli Distribution -- 4.3 Binomial Distribution -- 4.4 Geometric Distribution -- 4.5 Pascal (or Negative Binomial) Distribution -- 4.6 Hypergeometric Distribution -- 4.7 Poisson Distribution -- 4.8 Exponential Distribution -- 4.9 Erlang Distribution -- 4.10 Uniform Distribution -- 4.11 Normal Distribution -- 4.12 The Hazard Function -- 4.13 Chapter Summary -- 4.14 Problems -- Chapter 5. Multiple Random Variables -- 5.1 Introduction -- 5.2 Joint CDFs of Bivariate Random Variables -- 5.3 Discrete Random Variables -- 5.4 Continuous Random Variables -- 5.5 Determining Probabilities from a Joint CDF.

5.6 Conditional Distributions -- 5.7 Covariance and Correlation Coefficient -- 5.8 Many Random Variables -- 5.9 Multinomial Distributions -- 5.10 Chapter Summary -- 5.11 Problems -- Chapter 6. Functions of Random Variables -- 6.1 Introduction -- 6.2 Functions of One Random Variable -- 6.3 Expectation of a Function of One Random Variable -- 6.4 Sums of Independent Random Variables -- 6.5 Minimum of Two Independent Random Variables -- 6.6 Maximum of Two Independent Random Variables -- 6.7 Comparison of the Interconnection Models -- 6.8 Two Functions of Two Random Variables -- 6.9 Laws of Large Numbers -- 6.10 The Central Limit Theorem -- 6.11 Order Statistics -- 6.12 Chapter Summary -- 6.13 Problems -- Chapter 7. Transform Methods -- 7.1 Introduction -- 7.2 The Characteristic Function -- 7.3 The s-Transform -- 7.4 The z-Transform -- 7.5 Random Sum of Random Variables -- 7.6 Chapter Summary -- 7.7 Problems -- Chapter 8. Introduction to Random Processes -- 8.1 Introduction -- 8.2 Classification of Random Processes -- 8.3 Characterizing a Random Process -- 8.4 Crosscorrelation and Crosscovariance Functions -- 8.5 Stationary Random Processes -- 8.6 Ergodic Random Processes -- 8.7 Power Spectral Density -- 8.8 Discrete-Time Random Processes -- 8.9 Chapter Summary -- 8.10 Problems -- Chapter 9. Linear Systems with Random Inputs -- 9.1 Introduction -- 9.2 Overview of Linear Systems with Deterministic Inputs -- 9.3 Linear Systems with Continuous-Time Random Inputs -- 9.4 Linear Systems with Discrete-Time Random Inputs -- 9.5 Autoregressive Moving Average Process -- 9.6 Chapter Summary -- 9.7 Problems -- Chapter 10. Some Models of Random Processes -- 10.1 Introduction -- 10.2 The Bernoulli Process -- 10.3 Random Walk -- 10.4 The Gaussian Process -- 10.5 Poisson Process -- 10.6 Markov Processes -- 10.7 Discrete-Time Markov Chains.

10.8 Continuous-Time Markov Chains -- 10.9 Gambler's Ruin as a Markov Chain -- 10.10 Chapter Summary -- 10.11 Problems -- Chapter 11. Introduction to Statistics -- 11.1 Introduction -- 11.2 Sampling Theory -- 11.3 Estimation Theory -- 11.4 Hypothesis Testing -- 11.5 Curve Fitting and Linear Regression -- 11.6 Chapter Summary -- 11.7 Problems -- Appendix 1: Table for the CDF of the Standard Normal Random Variable -- Bibliography -- Index.