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Formulas: Cumulative Distribution Function (CDF) for the Binomial Distribution

Cumulative Distribution Function (CDF) for the Binomial Distribution Formulas

Below you will find descriptions and details for the 4 formulas that are used to compute cumulative distribution function (CDF) values for the binomial distribution.

Beta function:
Beta function formula
Binomial distribution cumulative distribution function (CDF):
Binomial distribution cumulative distribution function (CDF) formula
where x is the number of successes, n is the number of trials, p is the probability of a successful outcome, and I is the regularized lower incomplete beta function.
Lower incomplete beta function:
Lower incomplete beta function formula
Regularized lower incomplete beta function:
Regularized lower incomplete beta function formula
where the numerator is the lower incomplete beta function, and the denominator is the beta function.
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