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Introduction to probability /
Introduction to Probability, Second Edition, is written for upper-level undergraduate students in statistics, mathematics, engineering, computer science, operations research, actuarial science, biological sciences, economics, physics, and some of the social sciences. With his trademark clarity and e...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; Boston :
Elsevier Academic Press,
[2007]
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Machine generated contents note: ch. 1 Some Motivating Examples
- ch. 2 Some Fundamental Concepts
- 2.1. Some Fundamental Concepts
- 2.2. Some Fundamental Results
- 2.3. Random Variables
- 2.4. Basic Concepts and Results in Counting
- ch. 3 The Concept of Probability and Basic Results
- 3.1. Definition of Probability
- 3.2. Some Basic Properties and Results
- 3.3. Distribution of a Random Variable
- ch. 4 Conditional Probability and Independence
- 4.1. Conditional Probability and Related Results
- 4.2. Independent Events and Related Results
- ch. 5 Numerical Characteristics of a Random Variable
- 5.1. Expectation, Variance, and Moment-Generating Function of a Random Variable
- 5.2. Some Probability Inequalities
- 5.3. Median and Mode of a Random Variable
- ch. 6 Some Special Distributions
- 6.1. Some Special Discrete Distributions
- 6.1.1. Binomial Distribution
- 6.1.2. Geometric Distribution
- 6.1.3. Poisson Distribution
- 6.1.4. Hypergeometric Distribution
- 6.2. Some Special Continuous Distributions
- 6.2.1. Gamma Distribution
- 6.2.2. Negative Exponential Distribution
- 6.2.3. Chi-Square Distribution
- 6.2.4. Normal Distribution
- 6.2.5. Uniform (or Rectangular) Distribution
- 6.2.6. The basics of the Central Limit Theorem (CLT)
- ch. 7 Joint Probability Density Function of Two Random Variables and Related Quantities
- 7.1. Joint d.f. and Joint p.d.f. of Two Random Variables
- 7.2. Marginal and Conditional p.d.f.'s, Conditional Expectation and Variance
- ch. 8 Joint Moment-Generating Function, Covariance, and Correlation Coefficient of Two Random Variables
- 8.1. The Joint m.g.f. of Two Random Variables
- 8.2. Covariance and Correlation Coefficient of Two Random Variables
- 8.3. Proof of Theorem 1, Some Further Results
- ch. 9 Some Generalizations to k Random Variables, and Three Multivariate Distributions
- 9.1. Joint Distribution of k Random Variables and Related Quantities
- 9.2. Multinomial Distribution
- 9.3. Bivariate Normal Distribution
- 9.4. Multivariate Normal Distribution
- ch. 10 Independence of Random Variables and Some Applications
- 10.1. Independence of Random Variables and Criteria of Independence
- 10.2. The Reproductive Property of Certain Distributions
- 10.3. Distribution of the Sample Variance under Normality
- ch. 11 Transformation of Random Variables
- 11.1. Transforming a Single Random Variable
- 11.2. Transforming Two or More Random Variables
- 11.3. Linear Transformations
- 11.4. The Probability Integral Transform
- 11.5. Order Statistics
- ch. 12 Two Modes of Convergence, the Weak Law of Large Numbers, the Central Limit Theorem, and Further Results
- 12.1. Convergence in Distribution and in Probability
- 12.2. The Weak Law of Large Numbers and the Central Limit Theorem
- 12.2.1. Applications of the WLLN
- 12.2.2. Applications of the CLT
- 12.2.3. The Continuity Correction
- 12.3. Further Limit Theorems
- Ch. 13 An Overview of Statistical Inference
- 13.1. The Basics of Point Estimation
- 13.2. The Basics of Interval Estimation
- 13.3. The Basics of Testing Hypotheses
- 13.4. The Basics of Regression Analysis
- 13.5. The Basics of Analysis of Variance
- 13.6. The Basics of Nonparametric Inference.