HP 50G, User Manual

Page: 554 / 887

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