http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
1 online resource (xii, 387 pages) : illustrations
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 economy of language, the author explains important concepts of probability, while providing useful exercises and examples of real world applications for students to consider. After introducing fundamental probability concepts, the book proceeds to topics including special distributions, the joint probability density function, covariance and correlation coefficients of two random variables, and more. Demonstrates the applicability of probability to many human activities with examples and illustrationsDiscusses probability theory in a mathematically rigorous, yet accessible wayEach section provides relevant proofs, and is followed by exercises and useful hintsAnswers to even-numbered exercises are provided and detailed answers to all exercises are available to instructors on the book companion site.
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.
Includes bibliographical references and index.