The BINOMIAL function computes the probability that in a cumulative binomial (Bernoulli) distribution, a random variable *X* is greater than or equal to a user-specified value *V*, given *N* independent performances and a probability of occurrence or success *P* in a single performance:

This routine is written in the IDL language. Its source code can be found in the file binomial.pro in the lib subdirectory of the IDL distribution.

## Examples

Compute the probability of obtaining at least two 6s in rolling a die four times. The result should be 0.131944.

result = BINOMIAL(2, 4, 1.0/6.0)

PRINT, result

Compute the probability of obtaining exactly two 6s in rolling a die four times. The result should be 0.115741.

result = BINOMIAL(2, 4, 1./6.) - BINOMIAL(3, 4, 1./6.)

PRINT, result

Compute the probability of obtaining three or fewer 6s in rolling a die four times. The result should be 0.999228.

result = BINOMIAL(0, 4, 1./6.) - BINOMIAL(4, 4, 1./6.)

PRINT, result

## Syntax

*Result* = BINOMIAL(*V*,* N*,* P* [, /DOUBLE] [, /GAUSSIAN] )

## Return Value

This function returns a single- or double-precision floating point scalar or array that contains the value of the probability.

If all arguments are scalar, the function returns a scalar. If all arguments are arrays, the function matches up the corresponding elements of *V*, *N*, and *P*, returning an array with the same dimensions as the smallest array. If one argument is a scalar and the other arguments are arrays, the function uses the scalar value with each element of the arrays, and returns an array with the same dimensions as the smallest input array.

If any of the arguments are double-precision or if the DOUBLE keyword is set, the result is double-precision, otherwise the result is single-precision.

## Arguments

### V

A non-negative integer scalar or array specifying the minimum number of times the event occurs in *N* independent performances.

### N

A non-negative integer scalar or array specifying the number of performances.

### P

A non-negative single- or double-precision floating-point scalar or array, in the interval [0.0, 1.0], that specifies the probability of occurrence or success of a single independent performance.

### DOUBLE

Set this keyword to force the computation to be done in double-precision arithmetic.

## Examples

## Version History

Pre 4.0 |
Introduced |

8.7 |
Changed to use IBETA; deprecated GAUSSIAN keyword. |

## See Also

CHISQR_PDF, F_PDF, GAUSS_PDF, T_PDF, IBETA