Probability via Expectation
E695665
"Probability via Expectation" is a foundational textbook by Peter Whittle that develops probability theory with a strong emphasis on the role of expectation as the central conceptual tool.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Probability via Expectation canonical | 3 |
How this entity was disambiguated
This entity first appeared as the object of triple T7853057 — 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: Probability via Expectation Context triple: [Peter Whittle, notableWork, Probability via Expectation]
-
A.
Probability Theory
Probability Theory is a foundational branch of mathematics that studies random phenomena and quantifies uncertainty using concepts such as probability measures, random variables, and distributions.
-
B.
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.
-
C.
The Art of Probability for Scientists and Engineers
The Art of Probability for Scientists and Engineers is a textbook by mathematician Richard W. Hamming that presents probability theory with an emphasis on practical applications in science and engineering.
-
D.
Foundations of Probability
Foundations of Probability is a seminal textbook by mathematician Alfréd Rényi that presents a rigorous, axiomatic treatment of probability theory.
-
E.
The Theory of Probability
The Theory of Probability is Hans Reichenbach’s influential philosophical and mathematical treatise that helped establish a rigorous, frequency-based interpretation of probability within the logical empiricist tradition.
- 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: Probability via Expectation Target entity description: "Probability via Expectation" is a foundational textbook by Peter Whittle that develops probability theory with a strong emphasis on the role of expectation as the central conceptual tool.
-
A.
Probability Theory
Probability Theory is a foundational branch of mathematics that studies random phenomena and quantifies uncertainty using concepts such as probability measures, random variables, and distributions.
-
B.
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.
-
C.
The Art of Probability for Scientists and Engineers
The Art of Probability for Scientists and Engineers is a textbook by mathematician Richard W. Hamming that presents probability theory with an emphasis on practical applications in science and engineering.
-
D.
Foundations of Probability
Foundations of Probability is a seminal textbook by mathematician Alfréd Rényi that presents a rigorous, axiomatic treatment of probability theory.
-
E.
The Theory of Probability
The Theory of Probability is Hans Reichenbach’s influential philosophical and mathematical treatise that helped establish a rigorous, frequency-based interpretation of probability within the logical empiricist tradition.
- F. None of above. chosen
Statements (35)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
person ⓘ textbook ⓘ |
| approach | development of probability via expectation operators ⓘ |
| author | Peter Whittle ⓘ |
| conceptualFocus |
expectation as primary tool for defining probability
ⓘ
unification of discrete and continuous probability via expectation ⓘ |
| emphasis | expectation as central concept in probability ⓘ |
| field |
mathematics
ⓘ
probability theory ⓘ probability theory ⓘ stochastic processes ⓘ |
| hasAuthor | Peter Whittle ⓘ |
| intendedAudience |
students of economics
ⓘ
students of engineering ⓘ students of mathematics ⓘ students of statistics ⓘ |
| language | English ⓘ |
| notableWork | Probability via Expectation ⓘ |
| occupation | mathematician ⓘ |
| pedagogicalLevel |
advanced undergraduate
ⓘ
beginning graduate ⓘ |
| topic |
central limit theorem
ⓘ
conditional expectation ⓘ continuous probability ⓘ discrete probability ⓘ expectation ⓘ independence ⓘ laws of large numbers ⓘ measure-theoretic ideas in probability ⓘ moments of random variables ⓘ probability distributions ⓘ random variables ⓘ |
| use |
self-study reference
ⓘ
university course textbook ⓘ |
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: Probability via Expectation Description of subject: "Probability via Expectation" is a foundational textbook by Peter Whittle that develops probability theory with a strong emphasis on the role of expectation as the central conceptual tool.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.