Manuals/calci/POISSONDISTRIBUTED

POISSONDISTRIBUTED(Numbers,Lambda)

• $Numbers$ is the number of random numbers to display.
• $Lamda$ is the mean value.

Description

• This function shows the random variables of Poisson distribution.
• It is a discrete frequency distribution which gives the probability of a number of independent events occurring in a fixed time.
• A Poisson random variable is the number of successes that result from a Poisson experiment.
• The probability distribution of a Poisson random variable is called a Poisson distribution.
• Suppose we conduct a Poisson experiment, in which the average number of successes within a given region is $\mu$.
• Then, the Poisson probability is:

$P(x;\mu )={\frac {(e^{-\mu })(\mu ^{x})}{x!}}$

• where x is the actual number of successes that result from the experiment, and e is approximately equal to 2.71828.
• The Poisson distribution has the following properties:

1. The mean of the distribution is equal to $\mu$ .
2. The variance is also equal to $\mu$ .

• This function will give the result as error when b<0 and a value is not an integer.

Examples

1. POISSONDISTRIBUTED(3,3) = 2 1 3
2. POISSONDISTRIBUTED(5,45) = 37 39 45 35 47
3. POISSONDISTRIBUTED(7,67.45) = 79.45 65.45 75.45 72.45 83.45 74.45 77.45

See Also

• POISSON
• EXPONDIST

References

Poisson Probability Distribution

• List of Main Z Functions

• Z3 home