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probability of getting a success in any given repetition. The cumulative
distribution function for the binomial distribution is given by
nxxpnfxpnF
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
xf
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
xxfxF
x
k
λλ
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
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