Introduction to probability with R
- Includes bibliographical references (p. 355) and index.
- FOREWORD PREFACE Sets, Events, and Probability The Algebra of Sets The Bernoulli Sample Space The Algebra of Multisets The Concept of Probability Properties of Probability Measures Independent Events The Bernoulli Process The R Language Finite Processes The Basic Models Counting Rules Computing Factorials The Second Rule of Counting Computing Probabilities Discrete Random Variables The Bernoulli Process: Tossing a Coin The Bernoulli Process: Random Walk Independence and Joint Distributions Expectations The Inclusion-Exclusion Principle General Random Variables Order Statistics The Concept of a General Random Variable Joint Distribution and Joint Density Mean, Median and Mode The Uniform Process Table of Probability Distributions Scale Invariance Statistics and the Normal Distribution Variance Bell-Shaped Curve The Central Limit Theorem Significance Levels Confidence Intervals The Law of Large Numbers The Cauchy Distribution Conditional Probability Discrete Conditional Probability Gaps and Runs in the Bernoulli Process Sequential Sampling Continuous Conditional Probability Conditional Densities Gaps in the Uniform Process The Algebra of Probability Distributions The Poisson Process Continuous Waiting Times Comparing Bernoulli with Uniform The Poisson Sample Space Consistency of the Poisson Process Randomization and Compound Processes Randomized Bernoulli Process Randomized Uniform Process Randomized Poisson Process Laplace Transforms and Renewal Processes Proof of the Central Limit Theorem Randomized Sampling Processes Prior and Posterior Distributions Reliability Theory Bayesian Networks Entropy and Information Discrete Entropy The Shannon Coding Theorem Continuous Entropy Proofs of Shannon's Theorems Markov Chains The Markov Property The Ruin Problem The Network of a Markov Chain The Evolution of a Markov Chain The Markov Sample Space Invariant Distributions Monte Carlo Markov Chains appendix A: Random Walks Fluctuations of Random Walks The Arcsine Law of Random Walks Appendix B: Memorylessness and Scale-Invariance Memorylessness Self-Similarity References Index Exercises and Answers appear at the end of each chapter.
- (source: Nielsen Book Data)
- Publisher's Summary
- Based on a popular course taught by the late Gian-Carlo Rota of MIT, with many new topics covered as well, Introduction to Probability with R presents R programs and animations to provide an intuitive yet rigorous understanding of how to model natural phenomena from a probabilistic point of view. Although the R programs are small in length, they are just as sophisticated and powerful as longer programs in other languages. This brevity makes it easy for students to become proficient in R. This calculus-based introduction organizes the material around key themes. One of the most important themes centers on viewing probability as a way to look at the world, helping students think and reason probabilistically. The text also shows how to combine and link stochastic processes to form more complex processes that are better models of natural phenomena. In addition, it presents a unified treatment of transforms, such as Laplace, Fourier, and z; the foundations of fundamental stochastic processes using entropy and information; and an introduction to Markov chains from various viewpoints. Each chapter includes a short biographical note about a contributor to probability theory, exercises, and selected answers. The book has an accompanying website with more information.
(source: Nielsen Book Data)
- Supplemental links
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Table of contents
- Publication date
- Kenneth Baclawski.
- Chapman & Hall/CRC texts in statistical science series
- Available in another form
- Online version: Baclawski, Kenneth. Introduction to probability with R. Boca Raton, FL : Chapman & Hall/CRC, c2008 (OCoLC)681503827