Hypergeometric Distribution. Probability density function, cumulative distribution function, mean and variance
This calculator calculates hypergeometric distribution pdf, cdf, mean and variance for given parameters
In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of k successes (random draws for which the object drawn has a specified feature) in n draws, without replacement, from a finite population of size N that contains exactly K objects with that feature, wherein each draw is either a success or a failure. In contrast, the binomial distribution describes the probability of k successes in n draws with replacement. Wikipedia
Probability density function of the hypergeometric distribution is
,
where
is the number of combinations of m from n or binomial coefficient
Cumulative distribution function of the hypergeometric distribution is
,
where
is the generalized hypergeometric function
Mean or expected value for the hypergeometric distribution is
Variance is
The calculator below calculates the mean and variance of the negative binomial distribution and plots the probability density function and cumulative distribution function for given parameters n, K, N.
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