Integral_Theorem {ExpRep}

Integral Theorem of DeMoivre-Laplace

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

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.

See Also

Poisson_Theorem, Local_Theorem.

Examples

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)
  }