Introduction to probability with R. (2008)

• Record Type: Book
• Further Information: Note: Kenneth Baclawski.
• Other Names: Baclawski, Kenneth
• Contents: 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.
• Publisher Details: Place of publication not identified : Chapman and Hall/CRC
• Publication Date: 2008
• Extent: 1 online resource (384 pages), (92 illustrations)
• Subjects: 519.202855133; Probabilities; R (Computer program language) -- Mathematical models
• Languages: English
• ISBNs: 9781420065220
• Related ISBNs: 142006522X
• 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.