Mathematical Techniques of Applied Probability

¿PrefaceAcknowledgmentsChapter 1 Basic Probability 1.1 Introduction 1.2 Probability Measures 1.3 Conditional Probability and Independence 1.4 Random Variables and Their Distributions 1.5 Multivariate Random Variables and Their Distributions 1.6 Stochastic ProcessesChapter 2 Generating Functions 2.1 Introduction 2.2 Real Analysis-Sequences of Functions and Double Sequences 2.3 Properties of Generating Functions 2.4 Tail Probabilities 2.5 Convolutions 2.6 Compound Distributions 2.7 Derivation of Probability Distributions from Probabihty-Generating Functions 2.8 The Convergence of Sequences of Probability-Generating Functions 2.9 Solution of Difference Equations 2.10 Bivariate Generating FunctionsChapter 3 Recurrent Event Theory 3.1 Introduction and Definitions 3.2 Classification of Events 3.3 Basic Theorems for Recurrent Events 3.4 The Number of Occurrences of a Recurrent Event 3.5 General Recurrent Event Processes 3.6 An Application of Recurrent Event Theory: Success Runs in Bernoulli Trials 3.7 An Application of Recurrent Event Theory: Patterns in Bernoulli TrialsChapter 4 Matrix Techniques 4.1 Introduction and Basic Operations 4.2 Determinants, Inverses, Ranks, and Generalized Inverses 4.3 Solving Systems of Linear Equations 4.4 Vector Spaces and Diagonalization of Matrices 4.5 Matrix Analysis 4.6 Nonnegative Matrices 4.7 Infinite MatricesChapter 5 Markov Chains in Discrete Time-Basic Theory 5.1 Introduction and Basic Definitions 5.2 Classification of States 5.3 Decomposition of the State Space 5.4 Canonical Forms of the Transition Matrix of a Markov Chain 5.5 Limiting DistributionsReferencesIndex