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probability of getting a success in any given repetition. The cumulative
distribution function for the binomial distribution is given by
n
x
x
p
n
f
x
p
n
F
x
k
,...,
2
,
1
,
0
,)
,
,
(
)
,
,
(
0
=
=
∑
=
Poisson distribution
The probability mass function of the Poisson distribution is given by
∞
=
⋅
=
−
,...,
2
,
1
,
0
,
!
)
,
(
x
x
e
x
f
x
λ
λ
λ
.
In this expression, if the random variable X represents the number of
occurrences of an event or observation per unit time, length, area, volume,
etc., then the parameter l represents the average number of occurrences per
unit time, length, area, volume, etc. The cumulative distribution function for
the Poisson distribution is given by
∞
=
=
∑
=
,...,
2
,
1
,
0
,)
,
(
)
,
(
0
x
x
f
x
F
x
k
λ
λ
Next, use function DEFINE (
„à
) to define the following probability mass
functions (pmf) and cumulative distribution functions (cdf):
DEFINE(pmfb(n,p,x) = COMB(n,x)*p^x*(1-p)^(n-x))
DEFINE(cdfb(n,p,x) =
Σ
(k=0,x,pmfb(n,p,k)))
DEFINE(pmfp(
λ
,
x) = EXP(-
λ
)*
λ
^x/x!)
DEFINE(cdfp(
λ
,x) =
Σ
(k=0,x,pmfp(
λ
,x)))
The function names stand for:
•
pmfb: probability mass function for the binomial distribution
•
cdfb: cumulative distribution function for the binomial distribution
•
pmfp: probability mass function for the Poisson distribution
•
cdfp: cumulative distribution function for the Poisson distribution