Hypergeometric distribution

[ ( N − 1 ) N 2 ( N ( N + 1 ) − 6 K ( N − K ) − 6 n ( N − n ) ) + {displaystyle {Big [}(N-1)N^{2}{Big (}N(N+1)-6K(N-K)-6n(N-n){Big )}+{}} In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of k {displaystyle k} successes (random draws for which the object drawn has a specified feature) in n {displaystyle n} draws, without replacement, from a finite population of size N {displaystyle N} that contains exactly K {displaystyle 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 {displaystyle k} successes in n {displaystyle n} draws with replacement. In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of k {displaystyle k} successes (random draws for which the object drawn has a specified feature) in n {displaystyle n} draws, without replacement, from a finite population of size N {displaystyle N} that contains exactly K {displaystyle 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 {displaystyle k} successes in n {displaystyle n} draws with replacement. In statistics, the hypergeometric test uses the hypergeometric distribution to calculate the statistical significance of having drawn a specific k {displaystyle k} successes (out of n {displaystyle n} total draws) from the aforementioned population. The test is often used to identify which sub-populations are over- or under-represented in a sample. This test has a wide range of applications. For example, a marketing group could use the test to understand their customer base by testing a set of known customers for over-representation of various demographic subgroups (e.g., women, people under 30).