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

Description Usage Arguments Details Value Note Author(s) References See Also Examples

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

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

`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.

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.

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

Department of Mathematics. University of Oriente. Cuba.

Larisa Zamora and Jorge Diaz

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

Poisson_Theorem, Local_Theorem.

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)
  }

[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)
}