Bernoulli trials
E141077
Bernoulli trials are a sequence of independent experiments, each with exactly two possible outcomes (often called success and failure) and the same probability of success on every trial, forming the basis of the binomial distribution in probability theory.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Bernoulli trials canonical | 3 |
| Bernoulli process | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T1233825 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bernoulli trials Context triple: [Jakob Bernoulli, knownFor, Bernoulli trials]
-
A.
binomial theorem
The binomial theorem is a fundamental algebraic formula that provides a systematic way to expand powers of binomial expressions, playing a key role in combinatorics and mathematical analysis.
-
B.
Pascal's triangle
Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
-
C.
Bayes’ theorem
Bayes’ theorem is a fundamental result in probability theory that describes how to update the probability of a hypothesis based on new evidence.
-
D.
multinomial theorem
The multinomial theorem is a fundamental algebraic formula that generalizes the binomial theorem to express powers of sums with any number of terms using multinomial coefficients.
-
E.
Pascal's identity
Pascal's identity is a fundamental combinatorial formula that relates adjacent binomial coefficients and underlies many proofs and properties of binomial expansions.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Bernoulli trials Target entity description: Bernoulli trials are a sequence of independent experiments, each with exactly two possible outcomes (often called success and failure) and the same probability of success on every trial, forming the basis of the binomial distribution in probability theory.
-
A.
binomial theorem
The binomial theorem is a fundamental algebraic formula that provides a systematic way to expand powers of binomial expressions, playing a key role in combinatorics and mathematical analysis.
-
B.
Pascal's triangle
Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
-
C.
Bayes’ theorem
Bayes’ theorem is a fundamental result in probability theory that describes how to update the probability of a hypothesis based on new evidence.
-
D.
multinomial theorem
The multinomial theorem is a fundamental algebraic formula that generalizes the binomial theorem to express powers of sums with any number of terms using multinomial coefficients.
-
E.
Pascal's identity
Pascal's identity is a fundamental combinatorial formula that relates adjacent binomial coefficients and underlies many proofs and properties of binomial expansions.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
probability theory concept
ⓘ
stochastic process ⓘ |
| formsBasisOf | binomial distribution ⓘ |
| hasApplication |
Bernoulli process modeling
ⓘ
modeling success/failure processes over time ⓘ |
| hasAssociatedDistribution |
Bernoulli distribution
ⓘ
binomial distribution ⓘ |
| hasAssociatedRandomVariableType | Bernoulli random variable ⓘ |
| hasAssumption |
each trial has two mutually exclusive outcomes
ⓘ
trials are independent ⓘ trials have identical success probability ⓘ |
| hasCodingConvention |
0 for failure
ⓘ
1 for success ⓘ |
| hasFailureProbability | 1 - p ⓘ |
| hasFailureProbabilitySymbol | q ⓘ |
| hasHistoricalNameOrigin | named after Jacob Bernoulli ⓘ |
| hasKeyCondition |
outcome of one trial does not affect others
ⓘ
probability of success does not change from trial to trial ⓘ |
| hasNumberOfOutcomesPerTrial | 2 ⓘ |
| hasOutcome |
failure
ⓘ
success ⓘ |
| hasOutcomeSpacePerTrial | {0,1} ⓘ |
| hasParameter |
number of trials n
ⓘ
success probability p ⓘ |
| hasProperty |
constant success probability
ⓘ
identically distributed trials ⓘ independent trials ⓘ |
| hasSuccessProbabilitySymbol | p ⓘ |
| hasTypicalExample |
coin toss sequence
ⓘ
sequence of defective/non-defective item inspections ⓘ sequence of yes-no survey responses ⓘ |
| isBuildingBlockOf |
Bernoulli trials
self-linksurface differs
ⓘ
surface form:
Bernoulli process
Poisson process approximation via rare-event limits ⓘ |
| isSpecialCaseOf | sequence of independent identically distributed random variables ⓘ |
| relatedTo |
central limit theorem for binomial distribution
ⓘ
law of large numbers ⓘ |
| satisfiesRelation | p + q = 1 ⓘ |
| usedIn |
binomial experiments
ⓘ
clinical trial design ⓘ confidence interval estimation for proportions ⓘ hypothesis testing ⓘ quality control ⓘ reliability analysis ⓘ |
| usedToDerive |
binomial probability mass function
ⓘ
distribution of sample proportion ⓘ |
| usedToModel | number of successes in n independent trials ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Bernoulli trials Description of subject: Bernoulli trials are a sequence of independent experiments, each with exactly two possible outcomes (often called success and failure) and the same probability of success on every trial, forming the basis of the binomial distribution in probability theory.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Bernoulli process
this entity surface form:
Bernoulli process