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· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 확률과 통계 > 베이즈 분석
· ISBN : 9781498755092
· 쪽수 : 652쪽
목차
- Axioms of Probability
- Combinatorial Methods
- Conditional Probability and Independence
- Distribution Functions and Discrete Random Variables
- Special Discrete Distributions
- Continuous Random Variables
- Special Continuous Distributions
- Bivariate Distributions
- Multivariate Distributions
- More Expectations and Variances
- Sums of Independent Random Variables and Limit Theorems
- Stochastic Processes
Introduction
Sample Space and Events
Axioms of Probability
Basic Theorems
Continuity of Probability Function
Probabilities and Random Selection of Points from Intervals
What Is Simulation?
Chapter Summary
Review Problems
Self-Test on Chapter
Introduction
Counting Principle
Number of Subsets of a Set
Tree Diagrams
Permutations
Combinations
Stirling’s Formula
Chapter Summary
Review Problems
Self-Test on Chapter
Conditional Probability
Reduction of Sample Space
The Multiplication Rule
Law of Total Probability
Bayes’ Formula
Independence
Chapter Summary
Review Problems
Self-Test on Chapter
Random Variables
Distribution Functions
Discrete Random Variables
Expectations of Discrete Random Variables
Variances and Moments of Discrete Random Variables
Moments
Standardized Random Variables
Chapter Summary
Review Problems
Self-Test on Chapter
Bernoulli and Binomial Random Variables
Expectations and Variances of Binomial Random Variables
Poisson Random Variable
Poisson as an Approximation to Binomial
Poisson Process
Other Discrete Random Variables
Geometric Random Variable
Negative Binomial Random Variable
Hypergeometric Random Variable
Chapter Summary
Review Problems
Self-Test on Chapter
Probability Density Functions
Density Function of a Function of a Random Variable
Expectations and Variances
Expectations of Continuous Random Variables
Variances of Continuous Random Variables
Chapter Summary
Review Problems
Self-Test on Chapter
Uniform Random Variable
Normal Random Variable
Correction for Continuity
Exponential Random Variables
Gamma Distribution
Beta Distribution
Survival Analysis and Hazard Function
Chapter Summary
Review Problems
Self-Test on Chapter
Joint Distribution of Two Random Variables
Joint Probability Mass Functions
Joint Probability Density Functions
Independent Random Variables
Independence of Discrete Random Variables
Independence of Continuous Random Variables
Conditional Distributions
Conditional Distributions: Discrete Case
Conditional Distributions: Continuous Case
Transformations of Two Random Variables
Chapter Summary
Review Problems
Self-Test on Chapter
Joint Distribution of n > Random Variables
Joint Probability Mass Functions
Joint Probability Density Functions
Random Sample
Order Statistics
Multinomial Distributions
Chapter Summary
Review Problems
Self-Test on Chapter
Expected Values of Sums of Random Variables
Covariance
Correlation
Conditioning on Random Variables
Bivariate Normal Distribution
Chapter Summary
Review Problems
Self-Test on Chapter
Moment-Generating Functions
Sums of Independent Random Variables
Markov and Chebyshev Inequalities
Chebyshev’s Inequality and Sample Mean
Laws of Large Numbers
Central Limit Theorem
Chapter Summary
Review Problems
Self-Test on Chapter
Introduction
More on Poisson Processes
What Is a Queuing System?
PASTA: Poisson Arrivals See Time Average
Markov Chains
Classifications of States of Markov Chains
Absorption Probability
Period
Steady-State Probabilities
Continuous-Time Markov Chains
Steady-State Probabilities
Birth and Death Processes
Chapter Summary
Review Problems
Self-Test on Chapter
