Fundamentals of Probability with Stochastic Processes - with Stochastic Processes, 4th Edition - 9780429856280

Content: Cover
 Half title
 Title
 Copyrights
 Dedication
 Contents
 Preface
 Chapter 1 Axioms of Probability
 1.1 Introduction
 1.2 Sample Space and Events
 1.3 Axioms of Probability
 1.4 Basic Theorems
 1.5 Continuity of Probability Function
 1.6 Probabilities 0 and 1
 1.7 Random Selection of Points from Intervals
 1.8 What Is Simulation?
 Chapter 1 Summary
 Review Problems
 Self-Test on Chapter 1
 Chapter 2 Combinatorial Methods
 2.1 Introduction
 2.2 Counting Principle
 Number of Subsets of a Set
 Tree Diagrams
 2.3 Permutations
 2.4 Combinations
 2.5 Stirling's Formula
 Chapter 2 Summary. Review ProblemsSelf-Test on Chapter 2
 Chapter 3 Conditional Probability and Independence
 3.1 Conditional Probability
 Reduction of Sample Space
 3.2 The Multiplication Rule
 3.3 Law of Total Probability
 3.4 Bayes' Formula
 3.5 Independence
 Chapter 3 Summary
 Review Problems
 Self-Test on Chapter 3
 Chapter 4 Distribution Functions and 4 Discrete Random Variables
 4.1 Random Variables
 4.2 Distribution Functions
 4.3 Discrete Random Variables
 4.4 Expectations of Discrete Random Variables
 4.5 Variances and Moments of Discrete Random Variables
 Moments
 4.6 Standardized Random Variables. Chapter 4 SummaryReview Problems
 Self-Test on Chapter 4
 Chapter 5 Special Discrete Distributions
 5.1 Bernoulli and Binomial Random Variables
 Expectations and Variances of Binomial Random Variables
 5.2 Poisson Random Variable
 Poisson as an Approximation to Binomial
 Poisson Process
 5.3 Other Discrete Random Variables
 Geometric Random Variable
 Negative Binomial Random Variable
 Hypergeometric Random Variable
 Chapter 5 Summary
 Review Problems
 Self-Test on Chapter 5
 Chapter 6 Continuous Random Variables
 6.1 Probability Density Functions. 6.2 Density Function of a Function of a Random Variable6.3 Expectations and Variances
 Expectations of Continuous Random Variables
 Variances of Continuous Random Variables
 Chapter 6 Summary
 Review Problems
 Self-Test on Chapter 6
 Chapter 7 Special Continuous Distributions
 7.1 Uniform Random Variable
 7.2 Normal Random Variable
 Correction for Continuity
 7.3 Exponential Random Variables
 7.4 Gamma Distribution
 7.6 Survival Analysis and Hazard Function
 Chapter 7 Summary
 Review Problems
 Self-Test on Chapter 7
 7.5 Beta Distribution
 Chapter 8 Bivariate Distributions. 8.1 Joint Distributions of Two Random VariablesJoint Probability Mass Functions
 Joint Probability Density Functions
 8.2 Independent Random Variables
 Independence of Discrete Random Variables
 Independence of Continuous Random Variables
 8.3 Conditional Distributions
 Conditional Distributions: Discrete Case
 Conditional Distributions: Continuous Case
 8.4 Transformations of Two Random Variables
 Chapter 8 Summary
 Review Problems
 Self-Test on Chapter 8
 Chapter 9 Multivariate Distributions
 9.1 Joint Distributions of n>
 2 Random Variables
 Joint Probability Mass Functions.