hypergeometric distribution
Specialized/TechnicalFormal Academic/Technical
Definition
Meaning
A probability distribution that describes the probability of k successes in n draws, without replacement, from a finite population of size N that contains exactly K success states.
In statistics, it models scenarios of sampling without replacement, contrasting with the binomial distribution which models sampling with replacement. It's fundamental in quality control, card games, and ecological studies.
Linguistics
Semantic Notes
The term is a noun phrase referring to a specific, defined statistical model. It is not used metaphorically.
Dialectal Variation
British vs American Usage
Differences
No significant difference in meaning or usage. Spelling of related terms may follow national conventions (e.g., analyse/analyze).
Connotations
None beyond its technical definition.
Frequency
Equally rare outside statistics/probability contexts in both varieties.
Vocabulary
Collocations
Grammar
Valency Patterns
The hypergeometric distribution (is used/arises/applies) when...We model X using the hypergeometric distribution (with parameters N, K, n).Vocabulary
Synonyms
Weak
Vocabulary
Antonyms
Usage
Context Usage
Business
Used in quality assurance for lot acceptance sampling, e.g., 'The inspector used the hypergeometric distribution to determine the probability of finding defective items in the batch.'
Academic
Core concept in statistics, probability theory, and related research papers. Common in mathematics and science textbooks.
Everyday
Virtually never used. A layperson might encounter it in the context of calculating odds in certain card games.
Technical
Primary domain of use. Found in statistical software documentation, engineering reports, and scientific studies involving finite population sampling.
Examples
By Part of Speech
adjective
British English
- The hypergeometric model is appropriate here.
- We need the hypergeometric probabilities.
American English
- The hypergeometric model is appropriate here.
- We need the hypergeometric probabilities.
Examples
By CEFR Level
- In some games of chance, the hypergeometric distribution can be used to work out the odds.
- The quality control analyst applied the hypergeometric distribution to assess the likelihood of accepting a shipment with a known number of defects.
- Unlike the binomial distribution, the hypergeometric distribution accounts for the changing probabilities when sampling without replacement from a small, finite population.
Learning
Memory Aids
Mnemonic
Think HYPER-card-GAME: In a card game (like poker), you draw cards WITHOUT putting them back (no replacement). This 'hyper' specific game uses the hypergeometric distribution to calculate your odds.
Conceptual Metaphor
DRAWING FROM A LIMITED BAG: Conceptualised as reaching into a bag containing a fixed mix of two item types, taking out a handful, and calculating the chance of getting a specific mix.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid literal translation of parts like 'hyper-' or 'geometric'. The standard Russian term is 'гипергеометрическое распределение'. Do not confuse with 'geometric distribution' ('геометрическое распределение'), which is a different concept.
Common Mistakes
- Using it when sampling is with replacement (should use binomial).
- Confusing its parameters (N, K, n) order.
- Pronouncing 'hypergeometric' with the stress on 'per' instead of on 'ge' (ˌhaɪ.pər.ge.o.MET.ric).
Practice
Quiz
When is the hypergeometric distribution used instead of the binomial distribution?
FAQ
Frequently Asked Questions
The three parameters are: N (population size), K (number of success states in the population), and n (number of draws).
Calculating the probability of being dealt a certain number of hearts in a 5-card poker hand from a standard 52-card deck.
The binomial distribution models independent trials (with replacement), so the probability of success is constant. The hypergeometric models dependent trials (without replacement), so the probability changes with each draw.
It is defined for finite populations. For very large populations relative to sample size, it approximates the binomial distribution.