This chapter explores a number of models and problems based on sampling from a finite population. Sampling without replacement from a population of objects of various types leads to the hypergeometric and multivariate hypergeometric models. Sampling with replacement from a finite population leads naturally to the birthday and coupon-collector problems. Sampling without replacement form an ordered population leads naturally to the matching problem and to the study of order statistics.
- The Hypergeometric Distribution
- The Multivariate Hypergeometric Distribution
- Order Statistics
- The Matching Problem
- The Birthday Problem
- The Coupon Collector Problem
- Pólya's Urn Process
- The Secretary Problem
- Sampling with replacement (or sampling from an infinite population) leads to independent, identically distributed random variables. The chapter on Random Samples is a general study of such variables.
- Card games are based on sampling without replacement; dice games are based on sampling with replacement. The chapter on Games of Chance includes a number of such games.
- Multinomial Trials are based on sampling with replacement from a multi-type population.
- The problem of estimating parameters based on a random sample is studied in the chapter on Point Estimation.
Sources and Resources
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.—Bertrand Russell in a 1929 lecture