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Poisson distribution
The probability mass function of the Poisson distribution is given by
.
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
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:
Θ pmfb: probability mass function for the binomial distribution
Θ cdfb: cumulative distribution function for the binomial distribution
Θ pmfp: probability mass function for the Poisson distribution
Θ cdfp: cumulative distribution function for the Poisson distribution
Examples of calculations using these functions are shown next:
nxxpnfxpnF
x
k
,...,2,1,0,),,(),,(
0
==
∑
=
∞=
⋅
=
−
,...,2,1,0,
!
),( x
x
e
xf
x
λ
λ
λ
∞==
∑
=
,...,2,1,0,),(),(
0
xxfxF
x
k
λλ