Poisson distribution, Poisson distribution ,17-5 – HP 50g Graphing Calculator User Manual
Page 554
Page 17-5
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:
n
x
x
p
n
f
x
p
n
F
x
k
,...,
2
,
1
,
0
,)
,
,
(
)
,
,
(
0
=
=
∑
=
∞
=
⋅
=
−
,...,
2
,
1
,
0
,
!
)
,
(
x
x
e
x
f
x
λ
λ
λ
∞
=
=
∑
=
,...,
2
,
1
,
0
,)
,
(
)
,
(
0
x
x
f
x
F
x
k
λ
λ