Umfang:
1 Online-Ressource (x, 562 pages)
,
digital, PDF file(s).
Ausgabe:
Third edition
ISBN:
9781139206990
,
9786613685629
Inhalt:
Understanding Probability is a unique and stimulating approach to a first course in probability. The first part of the book demystifies probability and uses many wonderful probability applications from everyday life to help the reader develop a feel for probabilities. The second part, covering a wide range of topics, teaches clearly and simply the basics of probability. This fully revised third edition has been packed with even more exercises and examples and it includes new sections on Bayesian inference, Markov chain Monte-Carlo simulation, hitting probabilities in random walks and Brownian motion, and a new chapter on continuous-time Markov chains with applications. Here you will find all the material taught in an introductory probability course. The first part of the book, with its easy-going style, can be read by anybody with a reasonable background in high school mathematics. The second part of the book requires a basic course in calculus.
Anmerkung:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
,
Cover; Understanding Probability; Title; Copyright; Contents; Introduction; Preface; Modern probability theory; Probability theory and simulation; An outline; PART ONE: Probability in action; 1: Probability questions; Question 1. A birthday problem (3.1, 4.2.3); Question 2. Probability of winning streaks (2.1.3, 5.10.1); Question 3. A scratch-and-win lottery (4.2.3); Question 4. A lotto problem (4.2.3); Question 5. Hitting the jackpot (Appendix); Question 6. Who is the murderer? (8.3); Question 7. A coincidence problem (4.3); Question 8. A sock problem (Appendix)
,
Question 9. A statistical test problem (12.4)Question 10. The best-choice problem (2.3, 3.6); Question 11. The Monty Hall dilemma (6.1); Question 12. An offer you can't refuse - or can you? (9.6.3, 10.4.7); 2: Law of large numbers and simulation; 2.1 Law of large numbers for probabilities; 2.1.1 Coin-tossing; 2.1.2 Random walk; 2.1.3 The arc-sine law; 2.2 Basic probability concepts; 2.2.1 Random variables; 2.2.2 Probability in finite sample spaces; 2.3 Expected value and the law of large numbers; 2.3.1 Best-choice problem; 2.4 Drunkard's walk; 2.4.1 The drunkard's walk in higher dimensions
,
2.4.2 The probability of returning to the point of origin2.5 St. Petersburg paradox; 2.6 Roulette and the law of large numbers; 2.7 Kelly betting system; 2.7.1 Long-run rate of return; 2.7.2 Fractional Kelly; 2.7.3 Derivation of the growth rate; 2.8 Random-number generator; 2.8.1 Pitfalls encountered in randomizing; 2.8.2 The card shuffle; 2.9 Simulating from probability distributions; 2.9.1 Simulating from an interval; 2.9.2 Simulating from integers; 2.9.3 Simulating from a discrete distribution; 2.9.4 Random permutation; 2.9.5 Simulating a random subset of integers
,
2.9.6 Simulation and probability2.10 Problems; 3: Probabilities in everyday life; 3.1 Birthday problem; 3.1.1 Simulation approach; 3.1.2 Theoretical approach; 3.1.3 Another birthday surprise; 3.1.4 The almost-birthday problem; 3.1.5 Coincidences; 3.2 Coupon collector's problem; 3.2.1 Simulation approach; 3.2.2 Theoretical approach; 3.3 Craps; 3.3.1 Simulation approach; 3.3.2 Theoretical approach; 3.4 Gambling systems for roulette; 3.4.1 Doubling strategy; 3.4.2 Simulation approach; 3.4.3 Theoretical approach; 3.5 Gambler's ruin problem; 3.6 Optimal stopping; 3.7 The 1970 draft lottery
,
3.8 Problems4: Rare events and lotteries; 4.1 Binomial distribution; 4.2 Poisson distribution; 4.2.1 The origin of the Poisson distribution; 4.2.2 Applications of the Poisson model; 4.2.3 Poisson model for weakly dependent trials; 4.2.4 The Poisson process; 4.3 Hypergeometric distribution; 4.4 Problems; 5: Probability and statistics; 5.1 Normal curve; 5.1.1 Probability density function; 5.1.2 Normal density function; 5.1.3 Percentiles; 5.2 Concept of standard deviation; 5.2.1 Variance and standard deviation; 5.2.2 Independent random variables; 5.2.3 Illustration: investment risks
,
5.2.4 Waiting-time paradox
,
Literaturverz. S. 556 - 557
,
Includes bibliographical references and index
,
Systemvoraussetzungen: Internet-Zugriff, Adobe Acrobat Reader.
Weitere Ausg.:
ISBN 9781107658561
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Tijms, Henk C., 1944 - Understanding probability Cambridge [u.a.] : Cambridge Univ. Press, 2012 ISBN 9781107658561
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Wahrscheinlichkeitsrechnung
;
Analysis
;
Zufall
;
Wahrscheinlichkeitsrechnung
;
Analysis
;
Zufall
;
Electronic books
DOI:
10.1017/CBO9781139206990
URL:
https://doi.org/10.1017/CBO9781139206990
