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E-grāmata: Basic Probability: What Every Math Student Should Know

(Vrije Univ, The Netherlands)
  • Formāts: 132 pages
  • Izdošanas datums: 16-Apr-2019
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789811202377
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  • Formāts: 132 pages
  • Izdošanas datums: 16-Apr-2019
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • Valoda: eng
  • ISBN-13: 9789811202377
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'What makes this book unique among books of similar size and scope is that when the author decided to include something in the book, he has treated it in a way similar to the common practice in textbooks, with very detailed and reader-friendly explanations, fully worked-out examples, and even numerous exercises There are no prerequisites beyond second-semester calculus and the book can be used for self-study as well as in the classroom.'CHOICEWritten by international award-winning probability expert Henk Tijms, Basic Probability: What Every Math Student Should Know presents the essentials of elementary probability. The book is primarily written for high school and college students learning about probability for the first time. In a highly accessible way, a modern treatment of the subject is given with emphasis on conditional probability and Bayesian probability, on striking applications of the Poisson distribution, and on the interface between probability and computer simulation.In modern society, it is important to be able to critically evaluate statements of a probabilistic nature presented in the media in order to make informed judgments. A basic knowledge of probability theory is indispensable to logical thinking and statistical literacy. The book provides this knowledge and illustrates it with numerous everyday situations.
Preface v
Chapter 1 Combinatorics and Calculus for Probability
1(12)
1.1 Factorials and binomial coefficients
1(6)
1.2 Basic results from calculus
7(4)
Appendix: Poisson distribution as limit of the binomial distribution
11(2)
Chapter 2 Basics of Elementary Probability
13(40)
2.1 Foundation of probability
13(8)
2.2 The concept of conditional probability
21(5)
2.3 The law of conditional probability
26(2)
2.4 Conditional probability and Bayesian probability
28(9)
2.5 The concept of random variable
37(2)
2.6 Expected value and standard deviation
39(11)
Appendix: Proofs for expected value and standard deviation
50(3)
Chapter 3 Useful Probability Distributions with Applications
53(26)
3.1 The binomial and Poisson probability distributions
53(8)
3.2 The normal and exponential probability densities
61(14)
3.3 The chi-square test
75(4)
Chapter 4 Surprising World of Poisson Probabilities
79(10)
4.1 Fraud in a Canadian lottery
79(2)
4.2 Santa Claus and a baby whisperer
81(2)
4.3 Coupon collector's problem
83(6)
Chapter 5 Computer Simulation and Probability
89(22)
5.1 Introduction and random number generators
89(4)
5.2 Simulation tools
93(5)
5.3 Applications of computer simulation
98(4)
5.4 Statistical analysis of simulation output
102(6)
Appendix: Python programs for simulation
108(3)
Solutions to Selected Problems 111(10)
Index 121