Download Poisson Probabilities

Page 1 of 2
Poisson Distribution Notes
0502-PoissonDist.doc
Poisson Probabilities (Statdisk – found under Analysis)
A Poisson distribution is a discrete probability distribution
that applies to occurrences of some event over a specified
interval, such as time, area, distance, or some similar unit.
The occurrences must be random, independent, and
uniformly distributed. Poisson distribution has mean µ and
standard deviation of σ = µ .
1. Enter a value for the mean.
2. Click on the Evaluate button to obtain the results.
3. Click Plot to see the graph and click the Print button to
print the results.
NOTE: The mean of 0.929 is enter. After click Evaluate, the
results appear. Notice that the mean and variance are equal
because the standard deviation is the square root of the
mean. The x-values, P(x= ), P(x≤ ), and P(x≥ ) are given in
the four columns.
poissonpdf( (Poisson Distribution – using TI-84 calculator)
Syntax: poissonpdf(mean, x=)
probability the number of successes = 2 when the mean is 5
poissonpdf(0.929,2) equals 0.1704283575
TI-84 INSTRUCTIONS
2nd DISTR
C:poissonpdf(
ENTER
poisson(0.929,2)
ENTER
poissoncdf( (cumulative Poisson Distribution – using TI-84 calculator)
Syntax: poissoncdf(mean, ≤x)
probability the number of successes ≤ 2 when the mean is 5
poissoncdf(0.929,2) equals 0.9322839397
TI-84 INSTRUCTIONS
2nd DISTR
D:poissoncdf(
ENTER
poisson(0.929,2)
ENTER
By comparison, we see that the calculator values match those from Statdisk.
Page 2 of 2
Poisson Distribution Notes
0502-PoissonDist.doc
POISSON (Microsoft Excel – found under Function Category: Statistical)
Returns the Poisson distribution. A common application of the Poisson distribution is predicting the number of
events over a specific time, such as the number of cars arriving at a toll plaza in 1 minute.
Syntax
POISSON(x,mean,cumulative)
X is the number of events.
Mean is the expected numeric value.
Cumulative is a logical value that determines the form of the probability distribution returned. If
cumulative is TRUE (or 1), POISSON returns the cumulative Poisson probability that the
number of random events occurring will be between zero and x inclusive; if FALSE (or 0), it
returns the Poisson probability mass function that the number of events occurring will be exactly
x.
Remarks
•
If x is not an integer, it is truncated.
•
If x or mean is nonnumeric, POISSON returns the #VALUE! error value.
•
If x ≤ 0, POISSON returns the #NUM! error value.
•
If mean ≤ 0, POISSON returns the #NUM! error value.
•
POISSON is calculated as follows.
µ xe −µ
For cumulative = FALSE:
P ( x =) =
For cumulative = TRUE:
P (≤ x ) = ∑
x!
x
k =0
µ k e −µ
k!
Examples POISSON(x,mean,cumulative)
POISSON(2, .3, FALSE) equals 0.033337. This means the probability that x = 2 when the mean is 0.3.
POISSON(2, .3, TRUE) equals 0.996401. This means the probability that x ≤ 2 when the mean is 0.3.