# Integral_Theorem: Integral Theorem of DeMoivre-Laplace In ExpRep: Experiment Repetitions

## Description

Given n Bernoulli experiments, with success probability p, this function calculates the probability that a successful event occurs between linf and lsup times.

## Usage

 `1` ```Integral_Theorem(n = 100, p = 0.5, linf = 0, lsup = 50) ```

## Arguments

 `n` An integer value representing the number of 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). `linf` An integer value representing the minimum number of times that the successful event should happen. `lsup` An integer value representing the maximum number of times that the successful event should happen.

## 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 small. It is necessary that linf < lsup.

## Value

A real value representing the approximate probability that a successful event occurs between linf and lsup times, in n repetitions of a Bernoulli experiment.

## 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.

Poisson_Theorem, Local_Theorem.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```Prob<-Integral_Theorem(n=100,p=0.5,linf=0,lsup=50) Prob ## The function is currently defined as function (n = 100, p = 0.5, linf = 0, lsup = 50) { A <- (linf - n * p)/sqrt(n * p * (1 - p)) B <- (lsup - n * p)/sqrt(n * p * (1 - p)) P <- pnorm(B) - pnorm(A) return(P) } ```

### Example output

```[1] 0.5
function (n = 100, p = 0.5, linf = 0, lsup = 50)
{
A <- (linf - n * p)/sqrt(n * p * (1 - p))
B <- (lsup - n * p)/sqrt(n * p * (1 - p))
P <- pnorm(B) - pnorm(A)
return(P)
}
```

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