EXCEL Probability Distribution Functions
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function as opposed to simply typing it in as text.
I. Common Discrete Distributions
Binomial Distribution
=
BINOMDIST(
x
,
n
,
p
,False)
Probability of
x
successes in
n
trials with
P
(Success)=
p
n
x
p
p
x
n
x
n
p
p
x
n
x
X
P
x
n
x
x
n
x
,...,
1
,
0
)
1
(
)!
(
!
!
)
1
(
)
(
=


=

=
=


=
BINOMDIST(
x
,
n
,
p
,True)
Probability of at most
x
successes in
n
trials with
P
(Success)=
p
n
x
p
p
k
n
x
p
p
x
X
P
x
k
k
n
k
,
,
1
,
0
)
1
(
)
(
)
0
(
)
(
0
=

=
+
+
=
≤
∑
=

Geometric/Negative Binomial Distribution
=NEGBINOMDIST(
x
,
r
,
p
)
Probability of having
x
failures prior to the
r
th
success
in independent Bernoulli trials with
P
(Success)=
p
. This is equivalent to observing
the
r
th
success on the (
x+r
)
th
trial. Geometric distribution arises when
r
= 1.
,...
2
,
1
,...
2
,
1
,
0
)
1
(
1
1
=
=



+
r
x
p
p
r
r
x
x
r
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Poisson Distribution
=
POISSON(
x
,
λ
,False)
Probability of
x
outcomes when
X
~Poisson(
λ
)
,...
1
,
0
!
)
(
=
=
=

x
x
e
x
X
P
x
λ
λ
=
POISSON(
x
,
λ
,TRUE)
Probability of at most
x
outcomes when
X
~Poisson(
λ
)
,...
1
,
0
!
)
(
0
=
=
≤

=
∑
x
k
e
x
X
P
k
x
k
λ
λ
Hypergeometric Distribution
=HYPGEOMDIST(
x
,
n,k,N
)
Probability of
x
successes in
n
Trials in population
with
k
Successes in
N
elements
N
n
x
N
k
x
n
N
x
n
k
N
x
k
x
X
P
≤
≤
≤
≤
≤
≤


=
=
0
0
)
(
II. Common Continuous Distributions
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 Spring '08
 Staff
 Binomial, Probability

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