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Introduction to Probability with R [Kõva köide]

(Northeastern University, Boston, Massachusetts, USA)
  • Formaat: Hardback, 380 pages, kõrgus x laius: 234x156 mm, kaal: 1120 g, 11 Halftones, black and white; 92 Illustrations, black and white
  • Sari: Chapman & Hall/CRC Texts in Statistical Science
  • Ilmumisaeg: 24-Jan-2008
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1420065211
  • ISBN-13: 9781420065213
Teised raamatud teemal:
  • Formaat: Hardback, 380 pages, kõrgus x laius: 234x156 mm, kaal: 1120 g, 11 Halftones, black and white; 92 Illustrations, black and white
  • Sari: Chapman & Hall/CRC Texts in Statistical Science
  • Ilmumisaeg: 24-Jan-2008
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 1420065211
  • ISBN-13: 9781420065213
Teised raamatud teemal:
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.

Arvustused

beginners should find the informal and nonthreatening presentation of the basic ideas very useful A more advanced student could use the book as an extra source of intriguing mathematical examples, as could an instructor searching for interesting items to throw into a more conventional course. a very interesting book Technometrics, May 2009, Vol. 51, No. 2

Generally, I was very impressed with this text. It gives a sold introduction to probability with many interesting applications. One of its strengths is its material on stochastic processes. Jim Albert, Bowling Green State University, The American Statistician, May 2009, Vol. 63, No. 2

a welcome addition. The book is clearly written and very well-organized and it stems in part from a popular course at MIT taught by the late Gian-Carlo Rota, which was originally designed in conjunction with the author of this book. The book goes well beyond the MIT course in making extensive use of computation and R. It would serve as an exemplary test for the first semester of a two-semester course on probability and statistics. Introduction to Probability with R is a well-organized course in probability theory. Journal of Statistical Software, April 2009

This advanced undergraduate textbook is a pleasure to read and this reviewer will definitely consider it next time he teaches the subject. The programming language R is an open-source, freely downloadable software package that is used in the book to illustrate various examples. However, the book is well usable even if you do not have the time to include too much programming in your class. All programs of the book, and several others, are downloadable from the books website. the exercises of this book are a lot of fun! They often have some historical background, they tell a story, and they are never routine. Every chapter also starts with historical background, helping the student realize that this subject was developed by actual people. All classic topics that you would want to cover in an introductory probability class are covered. Another aspect in which the book stands out among the competition is that discrete probability gets its due treatment. Miklós Bóna, University of Florida, MAA Reviews, June 2008

a broad spectrum of probability and statistics topics ranging from set theory to statistics and the normal distribution to Poisson process to Markov chains. The author has covered each topic with an ample depth and with an appreciation of the problems faced by the modern world. The book contains a rich collection of exercises and problems an excellent introduction to the open source software R is given in the book. This book showcases interesting, classic puzzles throughout the text, and readers can also get a glimpse of the lives and achievements of important pioneers in mathematics.

From the Foreword, Tianhua Niu, Brigham and Womens Hospital, Harvard Medical School, and Harvard School of Public Health, Boston, Massachusetts, USA

Foreword xi
Preface xiii
Sets, Events and Probability
1(28)
The Algebra of Sets
2(3)
The Bernoulli Sample Space
5(2)
The Algebra of Multisets
7(1)
The Concept of Probability
8(1)
Properties of Probability Measures
9(2)
Independent Events
11(1)
The Bernoulli Process
12(2)
The R Language
14(5)
Exercises
19(3)
Answers to Selected Exercises
22(7)
Finite Processes
29(18)
The Basic Models
30(1)
Counting Rules
31(1)
Computing Factorials
32(1)
The Second Rule of Counting
33(2)
Computing Probabilities
35(3)
Exercises
38(4)
Answers to Selected Exercises
42(5)
Discrete Random Variables
47(40)
The Bernoulli Process: Tossing a Coin
49(12)
The Bernoulli Process: Random Walk
61(1)
Independence and Joint Distributions
62(2)
Expectations
64(3)
The Inclusion-Exclusion Principle
67(4)
Exercises
71(4)
Answers to Selected Exercises
75(12)
General Random Variables
87(32)
Order Statistics
91(2)
The Concept of a General Random Variable
93(3)
Joint Distribution and Joint Density
96(1)
Mean, Median and Mode
97(1)
The Uniform Process
98(4)
Table of Probability Distributions
102(2)
Scale Invariance
104(2)
Exercises
106(5)
Answers to Selected Exercises
111(8)
Statistics and the Normal Distribution
119(46)
Variance
120(6)
Bell-Shaped Curve
126(2)
The Central Limit Theorem
128(4)
Significance Levels
132(2)
Confidence Intervals
134(3)
The Law of Large Numbers
137(2)
The Cauchy Distribution
139(4)
Exercises
143(10)
Answers to Selected Exercises
153(12)
Conditional Probability
165(44)
Discrete Conditional Probability
166(4)
Gaps and Runs in the Bernoulli Process
170(3)
Sequential Sampling
173(4)
Continuous Conditional Probability
177(3)
Conditional Densities
180(2)
Gaps in the Uniform Process
182(4)
The Algebra of Probability Distributions
186(5)
Exercises
191(8)
Answers to Selected Exercises
199(10)
The Poisson Process
209(32)
Continuous Waiting Times
209(6)
Comparing Bernoulli with Uniform
215(5)
The Poisson Sample Space
220(8)
Consistency of the Poisson Process
228(1)
Exercises
229(6)
Answers to Selected Exercises
235(6)
Randomization and Compound Processes
241(34)
Randomized Bernoulli Process
242(1)
Randomized Uniform Process
243(2)
Randomized Poisson Process
245(2)
Laplace Transforms and Renewal Processes
247(4)
Proof of the Central Limit Theorem
251(1)
Randomized Sampling Processes
252(1)
Prior and Posterior Distributions
253(3)
Reliability Theory
256(3)
Bayesian Networks
259(4)
Exercises
263(3)
Answers to Selected Exercises
266(9)
Entropy and Information
275(28)
Discrete Entropy
275(7)
The Shannon Coding Theorem
282(3)
Continuous Entropy
285(7)
Proofs of Shannon's Theorems
292(5)
Exercises
297(1)
Answers to Selected Exercises
298(5)
Markov Chains
303(40)
The Markov Property
303(4)
The Ruin Problem
307(5)
The Network of a Markov Chain
312(2)
The Evolution of a Markov Chain
314(4)
The Markov Sample Space
318(4)
Invariant Distributions
322(5)
Monte Carlo Markov Chains
327(3)
Exercises
330(2)
Answers to Selected Exercises
332(11)
Random Walks
343(8)
Fluctuations of Random Walks
343(4)
The Aresine Law of Random Walks
347(4)
Memorylessness and Scale-Invariance
351(4)
Memorylessness
351(1)
Self-Similarity
352(3)
References 355(2)
Index 357


Kenneth Baclawski