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.
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