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9.4.3  The binomial distribution

The probability density function for the binomial distribution: binomial

If you perform an experiment n times where the probability of success each time is p, then the probability of exactly k successes is:

  binomial(n,k,p) = 
n
 
k

pk (1−p)nk     (1)

This determines the binomial distribution.

The binomial command computes the density function for the binomial distribution.


Examples.

The cumulative distribution function for the binomial distribution: binomial_cdf

The binomial_cdf command computes the cumulative distribution function for the binomial distribution.


Examples.

The inverse distribution function for the binomial distribution: binomial_icdf

The binomial_icdf command computes the inverse distribution function for the binomial distribution.


Example.
Input:

binomial_icdf(4,0.5,0.9)

Output:

3

Note that binomial_cdf(4,0.5,3)=0.9375, which is bigger than 0.9, while binomial_cdf(4,0.5,2)=0.6875, which is smaller than 0.9.


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