PDF — Binomial | CodeCogs

Evaluates the binomial distribution probability density function.

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Interface

#include <codecogs/statistics/distributions/discrete/binomial/pdf.h>

using namespace Statistics::Distributions::Discrete::Binomial;

double PDF(double p, int s, int n)

The binomial distribution gives the discrete probability distribution

$$P_p(s|n)$$

(1)

of obtaining exactly s successes out of n Bernoulli trials (where the result of each Bernoulli trial is true with probability p and false with probability <em>1-p</em>). The binomial distribution is therefore given by:

$$P_p(s|n) = \frac{n!}{s!(n-s)!} p^s (1-p)^{n-s}$$

(2)

References

MathWorld, http://mathworld.wolfram.com/BinomialDistribution.html

Example 1

#include<iostream>
#include<codecogs/statistics/distributions/discrete/binomial/pdf.h>
int main()
{
  std::cout << "binomial PDF: " << Statistics::Distributions::Discrete::Binomial::PDF(0.3,2,5) << std::endl;
  return 0;
}

Output:

binomial PDF: 0.3087

Parameters

is the probability of success on any one trial

is the number of successes

is the number of events

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Result –