## BINOMIAL

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.

### 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.

### Arguments

#### V

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

#### N

A non-negative integer 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.

### Keywords

#### DOUBLE

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

#### GAUSSIAN

Set this keyword to use the Gaussian approximation, by using the normalized variable Z = (V - NP)/SQRT(NP(1 - P)).

 Note
The Gaussian approximation is useful when N is large and neither P nor (1-P) is close to zero, where the binomial summation may overflow. If GAUSSIAN is not explicitly set, and the binomial summation overflows, then BINOMIAL will automatically switch to using the Gaussian approximation.

### 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)
```

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.)
```

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.)
```

### Version History

Introduced: Pre 4.0