Understanding ProbabilityCambridge University Press, 14 de juny 2012 - 562 pàgines 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. |
Continguts
| 9 | |
| 18 | |
Probabilities in everyday life | 75 |
Rare events and lotteries | 108 |
Probability and statistics | 142 |
Chance trees and Bayes rule | 212 |
ESSENTIALS OF PROBABILITY | 227 |
Conditional probability and Bayes | 256 |
Jointly distributed random variables | 360 |
Multivariate normal distribution | 382 |
Conditioning by random variables | 404 |
Generating functions | 435 |
Discretetime Markov chains | 459 |
Continuoustime Markov chains | 507 |
Appendix Counting methods and ex | 532 |
Bibliography | 556 |
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approximately assigned average balls bankroll Bayes Bayesian bets binomial birthday Brownian motion cards casino central limit theorem chance experiment Chapter choose conditional probability confidence interval continuous random variable continuous-time Markov chain definition denote desired probability dice difficult discrete random variable distributed random variable distribution with expected distribution with parameters dollars draw drunkard equal equations event example expected value exponential distribution fair coin find finite first five fixed follows formula given gives independent random variables infinite integers jackpot large numbers law of conditional law of large Let the random lottery Lotto Markov chain moment-generating function normal distribution occurs outcomes payoff player Poisson distribution Poisson process probability density function probability mass function probability theory Problem profit random number random walk result roll roulette Rule sample space satisfies Section sequence Solution stake standard deviation standard normal statistics strategy tickets tosses total number var(X variance verify