Science and Mathematics Faculty Publications

Title

To Replace or Not to Replace — That is the Question

Document Type

Article

Publication Date

2-25-2020

Journal Title

The College Mathematics Journal

ISSN

1931-1346

Volume

51

Issue

2

First Page

117

Last Page

123

DOI

https://doi.org/10.1080/07468342.2020.1698932

Abstract

In this paper, the authors consider the following urn model. An urn contains R red balls and W white balls. n balls are drawn successively at random according to the following sampling rule: if a red ball is selected on a single trial, then the ball is put back into the urn; if a white ball is selected, then it is removed from the urn. Let X denote the number of white balls in the whole sample of n balls. The authors derive an expression for the probability mass function of X and compare their result with those for the classical models of samplings with and without replacement (leading to the binomial and hypergeometric distributions, respectively).

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