# std::binomial_distribution

 Defined in header template< class IntType = int > class binomial_distribution; (since C++11)

Produces random non-negative integer values i, distributed according to discrete probability function:

P(i|t,p) =

t
p

· pi
· (1 − p)t−i

The value obtained is the number of successes in a sequence of t yes/no experiments, each of which succeeds with probability p.

## Contents

### Member functions

constructs new distribution
(public member function) 
resets the internal state of the distribution
(public member function) 
##### Generation
generates the next random number in the distribution
(public member function) 
##### Characteristics
returns the t distribution parameter (number of trials)
(public member function) 
returns the p distribution parameter (probability of a trial generating true)
(public member function) 
gets or sets the distribution parameter object
(public member function) 
returns the minimum potentially generated value
(public member function) 
returns the maximum potentially generated value
(public member function) 

### Non-member functions

 operator==operator!= compares two distribution objects (function)  operator<> performs stream input and output on pseudo-random number distribution (function) 

### Example

plot of binomial distribution with probability of success of each trial exactly 0.5, illustrating the relationship with the pascal triangle (the probabilities that none, 1, 2, 3, or all four of the 4 trials will be successful in this case are 1:4:6:4:1)

```#include <iostream>
#include <iomanip>
#include <string>
#include <map>
#include <random>
int main()
{
std::random_device rd;
std::mt19937 gen(rd());
// perform 4 trials, each succeeds 1 in 2 times
std::binomial_distribution<> d(4, 0.5);

std::map<int, int> hist;
for(int n=0; n<10000; ++n)
++hist[d(gen)];
for(auto p : hist)
std::cout << p.first <<
' ' << std::string(p.second/100, '*') << '\n';
}```

Output:

```0 ******
1 ************************
2 *************************************
3 *************************
4 ******```