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...
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| Format: | eBook |
| Language: | English |
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Amsterdam
Elsevier Academic Press
2007, [2007]©2007
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| Online Access: | |
| Collection: | Elsevier ScienceDirect eBooks - Collection details see MPG.ReNa |
Table of Contents:
- Includes bibliographical references and index
- 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