# Poisson_Theorem: Poisson Theorem. In ExpRep: Experiment Repetitions

## Description

Given n Bernoulli experiments, with success probability p (p small), this function calculates the approximate probability that a successful event occurs exactly m times.

## Usage

 `1` ```Poisson_Theorem(n, m, p) ```

## Arguments

 `n` An integer value representing the number of repetitions of the Bernoulli experiment. `m` An integer value representing the number of times that a successful event occurs in the n repetitions of the Bernoulli experiment. `p` A real value with the probability that a successful event will happen in any single Bernoulli experiment (called the probability of success).

## Details

Bernoulli experiments are sequences of events, in which successive experiments are independent and at each experiment the probability of appearance of a "successful" event (p) remains constant. The value of n must be high and the value of p must be very small.

## Value

A numerical value representing the approximate probability that a successful event occurs exactly m times.

## Note

Department of Mathematics. University of Oriente. Cuba.

## Author(s)

Larisa Zamora and Jorge Diaz

## References

Gnedenko, B. V. (1978). The Theory of Probability. Mir Publishers. Moscow.

Integral_Theorem, Local_Theorem.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```Prob<-Poisson_Theorem(n=100,m=50,p=0.002) Prob ## The function is currently defined as function (n, m, p) { landa <- n * p P <- dpois(m, landa) return(P) } ```

ExpRep documentation built on July 4, 2017, 9:45 a.m.