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Probabilities.BinomPDF Method (int, int, double)
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Binomial probability density function (PDF).

Syntax
C#
Visual Basic
public static double BinomPDF(int x, int N, double p);
Parameters
Parameters 
Description 
int x 
Function domain, integer, valid on closed interval [0,n]. 
int N 
Defines number of trials. n must be a positive integer. 
double p 
Defines success probability. p must lie on the [0,1] closed interval. 
Returns

the binomial probability density function (PDF).

Remarks

Calculates the binomial probability density function. The binomial probability density function is defined by the following equation: 

 

where q=1-p and I is the discrete interval [0,1,...n] on which the binomial CDF is not zero. The result of BinomPDF is the probability of observing x successes in n independent trials and where the probability of success in any given trial is p. 

To recognize a situation that involves a binomial random variable, following assumptions must be met:

  • The experiment consists of a fixed number, n, of Bernoulli trials that result in either success or failure.
  • The trials are identical and independent and therefore the probability of success p, remains the same from trial to trial.
  • The random variable x denotes the number of successes obtained in the n trials.
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