ExpRep (version 1.0)

Local_Theorem: Local Theorem of DeMoivre-Laplace

Description

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

Usage

Local_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).

Value

A real value representing the approximate probability that a successful event occurs exactly m times in n repetitions of a Bernoulli experiment.

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.

References

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

See Also

Integral_Theorem, Poisson_Theorem.

Examples

Prob<-Local_Theorem(n=100,m=50,p=0.02)
Prob

## The function is currently defined as
function (n, m, p) 
{
    a <- n * p
    b <- sqrt(a * (1 - p))
    x <- (m - a)/b
    P <- dnorm(x, 0, 1)/b
    return(P)
  }