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