Introduction to probability. ([2007])

• Record Type: Book
• Further Information: Note: George Roussas.
• Other Names: Roussas, George G
• Contents: 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.
• Publisher Details: Amsterdam Boston : Elsevier Academic Press
• Publication Date: 2007
• Copyright Date: 2007
• Extent: 1 online resource (xii, 387 pages), illustrations
• Subjects: 519.2; Probabilities -- Textbooks; Probabilities; Waarschijnlijkheidstheorie; Wahrscheinlichkeitsrechnung; Electronic books; Textbooks; Lehrbuch
• Languages: English
• ISBNs: 9780128000410; 0128000414; 9780128001981; 0128001984
• Related ISBNs: 0120885956; 9780120885954
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.