### Some Instructional Issues in Hypergeometric Distribution

#### Abstract

A brief introduction to sampling without replacement is presented. We represent the probability of a sample outcome in sampling without replacement from a finite population by three equivalent forms involving permutation and combination. Then it is used to calculate the probability of any number of successes in a given sample. The resulting forms are equivalent to the well known mass function of the hypergeometric distribution. Vandermonde’s identity readily justifies different forms of the mass function. One of the new form of the mass function embodies binomial coefficient showing much resemblance to that of binomial distribution. It also yields some interesting identities. Some other related issues are discussed.

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PDFDOI: http://dx.doi.org/10.18187/pjsor.v8i3.536

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#### Title

##### Some Instructional Issues in Hypergeometric Distribution

#### Keywords

##### Hypergeometric Distribution, Without Replacement

#### Description

A brief introduction to sampling without replacement is presented. We represent the probability of a sample outcome in sampling without replacement from a finite population by three equivalent forms involving permutation and combination. Then it is used to calculate the probability of any number of successes in a given sample. The resulting forms are equivalent to the well known mass function of the hypergeometric distribution. Vandermonde’s identity readily justifies different forms of the mass function. One of the new form of the mass function embodies binomial coefficient showing much resemblance to that of binomial distribution. It also yields some interesting identities. Some other related issues are discussed.

#### Date

##### 2012-07-01

#### Identifier

#### Source

Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810