# Hypergeometric distribution.docx - 1 Hypergeometric...

• 5

This preview shows page 1 - 3 out of 5 pages.

1 Hypergeometric distribution) . We consider here the situation where we sample individuals or objects from a finite population, and where these individuals can have a finite number of different properties , which we for convenience label {1 ,...,m }. The actual sample space E consists of the entire population and each individual has precisely one of the properties. Let N j denote the total number of individuals with property j that are in E – with j {1 ,... ,m } – and is then the total number of individuals in the population. If we independently sample X 1 ,...,X n from E completely at random without replacement the probability of getting X 1 = x 1 the first time is 1 /N and the probability for getting X 2 = x 2 =6 x 1 the second time is 1 / ( N −1) etc. Since we assume that we make independent samples the probability of getting x 1 ,...,x n E in n samples is . We define the transformation h : E n → {0 , 1 ,... ,n } m
2 given by 1(property( x i ) = j ) for x = ( x 1 ,...,x n ) E n . Thus h j ( x ) is the number of elements in x = ( x 1 ,...,x n ) that have property j . The distribution of