Handbook 5: The Hypergeometric Distribution
•
There are several types of random variables for which we can create
a formula to find
P
(
X
=
x
), rather than needing to construct the
complete probability distribution table.
•
One such type is called the
hypergeometric distribution
.
•
A random variable with a hypergeometric distribution has the follow
ing characteristics:
–
We have a collection of
N
objects, from which we will select
n
of
them, one at a time,
without replacement
.
–
The
N
objects can be divided into two types; there are
K
objects
of the first type, and the remainder (
N

K
objects) are of the
second type.
–
The random variable
X
is the number of objects selected which
are of the first type.
•
We have seen this type of experiment before. For example, recall the
BC49 lottery questions from section 7.4; we had
N
= 49 numbers,
of which
n
= 6 were to be selected, without replacement. These 49
numbers can be divided into two types; the
K
= 6 winning numbers,
and the
N

K
= 43 nonwinning numbers. We were concerned with
X
, the number of winning numbers selected.
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 Spring '11
 stephenlang
 Calculus, Probability, ﬁrst type

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