# 11. Finite Sampling Models

#### Summary

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.

#### Related Topics

• 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.

#### Quote

• 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