About This Book
1.Probability
1.1.Probability Model
1.2.Sample Space
1.3.Events
1.4.Probability of Events
1.5.Conditional Probability
1.6.Law of Total Probability
1.7.Bayes' Rule
1.8.Independence
1.9.Problems
2.Univariate Random Variables
2.1.Random Variables
2.2.Cumulative Distribution Function
2.3.Discrete Random Variables
2.4.Common Discrete Random Variables
2.5.Continuous Random Variables
2.6.Common Continuous Random Variables
2.7.Functions of Random Variables
2.8.Expectation of a Discrete Random Variable
2.9.Expectation of a Continuous Random Variable
2.10.Expectation of a Function of a Random Variable
2.11.Reference Tables
2.12.Problems
3.Multivariate Random Variables
3.1.Multivariate Random Variables
3.2.Multivariate Discrete Random Variables
3.3.Multivariate Continuous Random Variables
3.4.Marginal Distributions
3.5.Independence
3.6.Sums of Random Variables
3.7.Expectations
3.8.Problems
4.Conditional Probability and Expectations
4.1.Introduction.
4.2.Conditional Probability Mass Function.
4.3.Conditional Probability Density Function
4.4.Computing Probabilities by Conditioning
4.5.Conditional Expectations
4.6.Computing Expectations by Conditioning
4.7.Problems
5.Discrete-Time Markov Models
5.1.What Is a Stochastic Process?
5.2.Discrete-Time Markov Chains
5.3.Examples of Markov Models
5.4.Transient Distributions
5.5.Occupancy Times
5.6.Limiting Behavior
5.7.Cost Models.
5.7.1.Expected Total Cost Over a Finite Horizon
5.7.2.Long-Run Expected Cost Per Unit Time
5.8.First Passage Times
5.9.Problems
6.Continuous-Time Markov Models
6.1.Continuous-Time Stochastic Processes
6.2.Continuous-Time Markov Chains
6.3.Exponential Random Variables
6.4.Examples of CTMCs: I
6.5.Poisson Processes
6.6.Examples of CTMCs: II
6.7.Transient Analysis: Uniformization
6.8.Occupancy Times
6.9.Limiting Behavior
……
7.Generalized Markov Models
8.Queueing Models
9.Optimal Design
10.Optimal Control
Answers to Selected Problems
Bibliography
Index
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