# Binomial Distribution

 Probability Home Binomial Distribution

The cumulative distribution function of a random variable X distributed according to the Binomial distribution has zero slope everywhere except where a jump occurs,
F(x) = P(X ≤ x), given by
F(x) =
 0 for x < 0 Σi=0[x] Cni p i (1 - p) n-i for 0 ≤ x ≤ n 1 for x > n

The corresponding probability point distribution, f(i), i = 0,...,n, is
f(i) =
 Cni p i (1 - p) n-i for i = 0,...,n 0 elsewhere

#### Function List

• double Binomial_Cumulative_Distribution( int n, int k, double p )

This function returns F(k) where F(k) is described above.

• double Binomial_Point_Distribution( int n, int k, double p )

This function returns f(k) where f(k) is described above.

• void Binomial_Distribution_Tables( int n, double p, double* pr, double* cumulative )

This function returns f(k) where f(k) is described above for k = 0,...,n in the array pr and returns F(k) where F(k) is described above for k = 0,...,n in the array cumulative.

#### Source Code

C source code is available for these routines: