MathLiveHypergeometric distribution
Gives the probability of drawing exactly x successes when sampling n items without replacement from a finite population of N items containing M successes. It is used for counting-type sampling problems such as drawing defective items from a lot.
P(X = x) = \frac{\binom{M}{x}\binom{N-M}{n-x}}{\binom{N}{n}}What the symbols mean
| discrete random variable counting the number of successes in the sample | |
| number of successes observed in the sample | |
| population size, with N \geq 1 | |
| number of success items in the population, with 0 \leq M \leq N-1 | |
| sample size drawn without replacement, with 1 \leq n \leq N | |
| binomial coefficient, the number of ways to choose b items from a |
About this formula
- FieldStatistics
- TopicProbability distributions
- LevelUniversity
- Also calledhypergeometric probability mass function, hypergeometric pmf, sampling without replacement probability, probability of x successes without replacement, hypergeometric formula
- SourceWikidata Q730600
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