Chargement en cours…
Understanding Probability.
Using everyday examples to demystify probability, this classic is now in its third edition with new chapters, exercises and examples.
| Cote: | Libro Electrónico |
|---|---|
| Auteur principal: | |
| Format: | Électronique eBook |
| Langue: | Inglés |
| Publié: |
Cambridge :
Cambridge University Press,
2012.
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| Édition: | 3rd ed. |
| Sujets: | |
| Accès en ligne: | Texto completo |
Table des matières:
- 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.