Local_Theorem: Local Theorem of DeMoivre-Laplace In ExpRep: Experiment Repetitions

Description

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

Usage

 `1` ```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).

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.

Value

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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```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) } ```