mathematical expectation: meaning, definition, pronunciation and examples
C2Formal, Technical, Academic
Quick answer
What does “mathematical expectation” mean?
The theoretical average value of a random variable, calculated as the sum of all possible values each multiplied by their probability of occurrence.
Audio
Pronunciation
Definition
Meaning and Definition
The theoretical average value of a random variable, calculated as the sum of all possible values each multiplied by their probability of occurrence.
In probability theory and statistics, it represents the long-run average outcome of a random experiment if repeated many times. It is a fundamental concept in decision theory, economics, and risk assessment.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or definitional differences. The term is used identically in technical contexts.
Connotations
Identical technical connotations in both varieties.
Frequency
Equally common in academic and technical writing in both regions.
Grammar
How to Use “mathematical expectation” in a Sentence
The mathematical expectation of [random variable] is [value].To calculate the mathematical expectation of [noun phrase].[Subject] has a mathematical expectation of [value].Vocabulary
Collocations
Examples
Examples of “mathematical expectation” in a Sentence
verb
British English
- One must first mathematically expect the value before analysing variance.
- The model mathematically expects a profit over the long term.
American English
- You need to mathematically expect the outcome before assessing risk.
- The process mathematically expects a certain failure rate.
adverb
British English
- The result was mathematically expected given the initial conditions.
- The system performs mathematically expectably over time.
American English
- The outcome was mathematically expected based on the probabilities.
- The device fails mathematically expectably after 10,000 cycles.
adjective
British English
- The expectation calculation followed a strictly mathematical procedure.
- They presented a mathematical-expectation model for the market.
American English
- The expectation value was derived using mathematical methods.
- We reviewed the mathematical-expectation framework of the theory.
Usage
Meaning in Context
Business
Used in quantitative finance for pricing models and risk assessment (e.g., 'The mathematical expectation of the portfolio's return guides our investment strategy.').
Academic
Core concept in probability, statistics, and related fields (e.g., 'The proof relies on the properties of mathematical expectation.').
Everyday
Virtually never used in everyday conversation.
Technical
Fundamental in actuarial science, engineering reliability, and game theory (e.g., 'The algorithm minimises the mathematical expectation of error.').
Vocabulary
Synonyms of “mathematical expectation”
Vocabulary
Antonyms of “mathematical expectation”
Watch out
Common Mistakes When Using “mathematical expectation”
- Using it to mean a personal hope or guess (e.g., 'My mathematical expectation is that it will rain').
- Confusing it with the 'most likely' (mode) or 'middle' (median) value.
FAQ
Frequently Asked Questions
Yes, in probability and statistics, 'mathematical expectation' and 'expected value' are synonymous terms.
Yes, absolutely. For example, the expectation of a die roll is 3.5, but you can never roll a 3.5.
No. It is a theoretical long-run average, not a prediction for any single trial.
It is crucial in insurance (actuarial science), finance (derivative pricing), economics (decision theory), and quality control (statistical process control).
The theoretical average value of a random variable, calculated as the sum of all possible values each multiplied by their probability of occurrence.
Mathematical expectation is usually formal, technical, academic in register.
Mathematical expectation: in British English it is pronounced /ˌmæθ.əˌmæt.ɪ.kəl ˌek.spekˈteɪ.ʃən/, and in American English it is pronounced /ˌmæθ.əˌmæt̬.ɪ.kəl ˌek.spekˈteɪ.ʃən/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “None. This is a technical term not used idiomatically.”
Learning
Memory Aids
Mnemonic
Think of a MATHEMATICIAN at a casino EXPECTING to calculate the average payout over thousands of bets, not predicting the next spin.
Conceptual Metaphor
THEORETICAL AVERAGE IS A PREDICTED CENTRE (The expectation is the 'centre of mass' of a probability distribution).
Practice
Quiz
What is the primary field of study for 'mathematical expectation'?