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

✍ Scribed by Ghahramani, Saeed

• Publisher: CRC Press
• Year: 2019
• Tongue: English
• Leaves: 653
• Edition: Fourth edition
• Category: Library

✦ Table of Contents

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&gt
2 Random Variables
Joint Probability Mass Functions.

✦ Subjects

Probabilities.;Stochastic processes.;MATHEMATICS -- Applied.;MATHEMATICS -- Probability & Statistics -- General.