Introduction to Probability
Edition: Second Edition
Publisher: Athena Scientific
Published: 2008
Place of publication: Belmont (MA), USA
Language: eng
Format: Hardcover
Number of pages: 532
ISBN-13: 9781886529236
Copyright date: 2002, 2008
Table of contents: label: 1. Sample Space and Probability
title: 1; label: 1.1. Sets
title: 3; label: 1.2. Probabilistic Models
title: 6; label: 1.3. Conditional Probability
title: 18; label: 1.4. Total Probability Theorem and Bayes' Rule
title: 28; label: 1.5. Independence
title: 34; label: 1.6. Counting
title: 44; label: 1.7. Summary and Discussion
title: 51; label: Problems
title: 53; label: 2. Discrecte Random Variables
title: 71; label: 2.1. Basic Concepts
title: 72; label: 2.2. Probability Mass Functions
title: 74; label: 2.3. Functions of Random Variables
title: 80; label: 2.4. Expectation, Mean and Variance
title: 81; label: 2.5. Joint PMFs of Multiple Random Variables
title: 92; label: 2.6. Conditioning
title: 97; label: 2.7. Independence
title: 109; label: 2.8. Summary and Discussion
title: 115; label: Problems
title: 119; label: 3. General Random Variables
title: 139; label: 3.1. Continuous Random Variables and PDFs
title: 140; label: 3.2. Cumulative Distribution Functions
title: 148; label: 3.3. Normal Random Variables
title: 153; label: 3.4. Joint PDFs of Multiple Random Variables
title: 158; label: 3.5. Conditioning
title: 164; label: 3.6. The Continuous Bayes' Rule
title: 178; label: 3.7. Summary and Discussion
title: 182; label: Problems
title: 184; label: 4. Further Topics on Random Variables
title: 201; label: 4.1. Derived Distributions
title: 202; label: 4.2. Covariance and Correlation
title: 217; label: 4.3. Conditional Expectation and Variance Revisited
title: 222; label: 4.4. Transforms
title: 229; label: 4.5. Sum of a Random Number of Independent Random Variables
title: 240; label: 4.6. Summary and Discussion
title: 244; label: Problems
title: 246; label: 5. Limit Theorems
title: 263; label: 5.1. Markov and Chebyshev Inequalities
title: 265; label: 5.2. The Weak Law of Large Numbers
title: 269; label: 5.3. Convergence in Probability
title: 271; label: 5.4. The Central Limit Theorem
title: 273; label: 5.5. The Strong Law of Large Numbers
title: 280; label: 5.6. Summary and Discussion
title: 282; label: Problems
title: 284; label: 6. The Bernoulli and Poisson Processes
title: 295; label: 6.1. The Bernoulli Process
title: 297; label: 6.2. The Poisson Process
title: 309; label: 6.3. Summary and Discussion
title: 324; label: Problems
title: 326; label: 7. Markov Chains
title: 339; label: 7.1. Discrete-Time Markov Chains
title: 340; label: 7.2. Classification of States
title: 346; label: 7.3. Steady-State Behavior
title: 352; label: 7.4. Absorption Probabilities and Expected Time to Absorption
title: 362; label: 7.5. Continous-Time Markov Chains
title: 369; label: 7.6. Summary and Discussion
title: 378; label: Problems
title: 380; label: 8. Bayesian Statistical Inference
title: 407; label: 8.1. Bayesian Inference and the Posterior Distribution
title: 412; label: 8.2. Point Estimation, Hypothesis Testing, and the MAP Rule
title: 420; label: 8.3. Bayesian Least Mean Squares Estimation
title: 430; label: 8.4. Bayesian Linear Least Mean Squares Estimation
title: 437; label: 8.5. Summary and Discussion
title: 444; label: Problems
title: 446; label: 9. Classical Statistical Inference
title: 459; label: 9.1. Classical Parameter Estimation
title: 462; label: 9.2. Linear Regression
title: 477; label: 9.3. Binary Hypothesis Testing
title: 486; label: 9.4. Significance Testing
title: 496; label: 9.5. Summary and Discussion
title: 505; label: Problems
title: 507; label: Index
title: 521