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--- hypergeometric_distribution [2023/04/12 16:21]
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-====== Hypergeometric Distribution ======
-In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the number of successes in a sequence of n draws from a finite population without replacement.
-There is a shipment of M objects in which K are defective. The hypergeometric distribution describes the probability that in a sample of n distinctive objects drawn from the shipment exactly x objects are defective.
-In general, if a random variable X follows the hypergeometric distribution with parameters M, K and n, then the probability of getting exactly x successes is given by
-f(x,M,K,n) = over(K,x)//over(M-k,n-x)/over(M,n)//
-where  over(n,k) = n!/(k!//(n-k)!)//
-The formula can be understood as follows: There are over(M,n) possible samples (without replacement). There are over(K,x) ways to obtain x defective objects and there are over(M-k,n-x) ways to fill out the rest of the sample with non-defective objects.
-The fact that the sum of the probabilities, as x runs through the range of possible values, is equal to 1, is essentially Vandermonde’s identity from combinatorics.
-support max(0,K+n-M) <= x <= min(K,n)
-^Parameter^Description                                                      ^Default value^
-|M        |Size of the population                                           |100.0        |
-|K        |Number of items with the desired characteristic in the population|50.0         |
-|n        |Number of samples drawn                                          |20.0         |

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