## RandomVariables Class BinomialVariable

```java.lang.Object
Statistics.RandomVariable
RandomVariables.BinomialVariable
```

public class BinomialVariable
extends RandomVariable

Binomial B(n,p) variable X. A trial with probability p of success is repeated n times. X is the number of successes.

 Constructor Summary ```BinomialVariable(int n, double p)```           Parameters of the binomial distribution:,/p>

 Method Summary ` double` `analyticMean()`           Unconditional mean given by exact formula. ` double` `analyticVariance()`           Unconditional variance given by exact formula. ` cern.jet.random.Binomial` `getBinomialDistribution()`           The underlying `cern.jet.random.Binomial` Binomial distribution. ` double` `getValue(int t)`           A new sample from the distribution of X conditioned on information available at time t. `static void` `main(java.lang.String[] args)`           Allocates a Binomial variable and compares the analytic mean and variance to Monte Carlo mean and variance over a sample of size 100,000.

 Methods inherited from class Statistics.RandomVariable `analyticCentralMoment, analyticConditionalCentraMoment, analyticConditionalMean, analyticConditionalMoment, analyticConditionalVariance, analyticMoment, basicHistogram, centered_X, conditionalEmpiricalDistribution, conditionalExpectation, conditionalExpectation, conditionalExpectation, conditionalExpectation, conditionalExpectation, conditionalHistogram, conditionalHistogram, conditionalMeanAndStandardDeviation, conditionalMeanAndStandardDeviation, conditionalMeanAndStandardDeviation, conditionalMeanAndStandardDeviation, conditionalMoment, conditionalVariance, cumulativeDistributionFunction, displayConditionalHistogram, displayConditionalHistogram, displayConditionalHistogram, displayConditionalHistogram, displayHistogram, displayHistogram, displayHistogram, displayHistogram, div, empiricalDistribution, expectation, expectation, expectation, expectation, expectation, fillSampleSet, get_empiricalDistributionIsInitialized, get_hasAnalyticCentralMoment, get_hasAnalyticMean, get_hasAnalyticMoment, get_hasAnalyticVariance, get_hasConditionalAnalyticCentralMoment, get_hasConditionalAnalyticMean, get_hasConditionalAnalyticMoment, get_hasConditionalAnalyticVariance, histogram, histogram, initEmpiricalDistribution, meanAndStandardDeviation, meanAndStandardDeviation, meanAndStandardDeviation, meanAndStandardDeviation, minus, mult, plus, quantile, scale, setHasAnalyticMean, setHasAnalyticVariance, variance`

 Methods inherited from class java.lang.Object `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

 Constructor Detail

### BinomialVariable

```public BinomialVariable(int n,
double p)```

Parameters of the binomial distribution:,/p>

Parameters:
`n` - number of trials.
`p` - probability of success.
 Method Detail

### analyticMean

`public double analyticMean()`
Description copied from class: `RandomVariable`

Unconditional mean given by exact formula.

Since in general there are no analytic formulas the default is an error message and program abort. Override this in special cases where analytic formulas do exist.

Overrides:
`analyticMean` in class `RandomVariable`

### analyticVariance

`public double analyticVariance()`
Description copied from class: `RandomVariable`

Unconditional variance given by exact formula.

Since in general there are no analytic formulas the default is an error message and program abort. Override this in special cases where analytic formulas do exist.

Overrides:
`analyticVariance` in class `RandomVariable`

### getBinomialDistribution

`public cern.jet.random.Binomial getBinomialDistribution()`
The underlying `cern.jet.random.Binomial` Binomial distribution. Much additional functionality. See the javdoc of the `colt` distribution.

### getValue

`public double getValue(int t)`
Description copied from class: `RandomVariable`

A new sample from the distribution of X conditioned on information available at time t.

This is the crucial method defining the random variable and information structure.

Specified by:
`getValue` in class `RandomVariable`
Parameters:
`t` - time - ingnored no sense of time defined (no conditioning in this context).

### main

`public static void main(java.lang.String[] args)`
Allocates a Binomial variable and compares the analytic mean and variance to Monte Carlo mean and variance over a sample of size 100,000. A smoothed histogram is shown also.

WARNING: histogram is smoothed, smooths out the discrete nature of the distribution.