probability distribution: meaning, definition, pronunciation and examples
LowTechnical / Academic
Quick answer
What does “probability distribution” mean?
A mathematical function that describes the likelihood of obtaining the possible values that a random variable can take.
Audio
Pronunciation
Definition
Meaning and Definition
A mathematical function that describes the likelihood of obtaining the possible values that a random variable can take.
In broader usage, it can refer to any formal or informal description of how probabilities are spread across different outcomes or categories in a system.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Spelling follows respective conventions (e.g., 'analyse' in UK vs. 'analyze' in US academic texts).
Connotations
Identical technical connotations in both varieties.
Frequency
Equally rare in general discourse and equally common in technical fields like statistics, engineering, and data science in both regions.
Grammar
How to Use “probability distribution” in a Sentence
The probability distribution of [random variable]A probability distribution for [outcomes/events]To follow a [named] probability distributionTo have a probability distribution that is [adjective]Vocabulary
Collocations
Examples
Examples of “probability distribution” in a Sentence
verb
British English
- The data appear to be distributed according to a Poisson model.
- We need to distribute the probabilities across these categories.
American English
- The errors are distributed normally.
- We distributed the probability mass evenly.
adverb
British English
- The scores were distributed normally.
- The values are distributed binomially.
American English
- The particles were distributed uniformly.
- The data are distributed approximately log-normally.
adjective
British English
- The distributional assumptions of the model were checked.
- He specialises in probabilistic modelling.
American English
- The distributional properties are key.
- This is a probabilistic forecast.
Usage
Meaning in Context
Business
Used in risk analysis, forecasting, and quantitative finance to model uncertain outcomes like sales or market returns.
Academic
Fundamental concept in statistics, probability theory, physics, engineering, and data science for formalising randomness.
Everyday
Virtually never used in everyday conversation outside of technical explanations.
Technical
The precise, formal term for describing how probability is allocated across a sample space.
Vocabulary
Synonyms of “probability distribution”
Strong
Neutral
Weak
Vocabulary
Antonyms of “probability distribution”
Watch out
Common Mistakes When Using “probability distribution”
- Using 'probability distribution' to refer to the frequency distribution of actual observed data (instead of 'frequency distribution' or 'empirical distribution').
- Saying 'the probability distribution is high' (incorrect) instead of 'the probability is high' or 'the distribution has a high mean'.
FAQ
Frequently Asked Questions
A probability distribution is a theoretical model describing the likelihood of outcomes for a random variable. A frequency distribution summarises actual observed counts or frequencies from collected data.
It is countable. You can have one probability distribution or compare several different probability distributions.
Yes. For categorical data (e.g., colours, brands), the distribution assigns probabilities to each category, often called a categorical or multinomial distribution.
The two main types are discrete probability distributions (for countable outcomes, like dice rolls) and continuous probability distributions (for measurable outcomes, like height or time).
A mathematical function that describes the likelihood of obtaining the possible values that a random variable can take.
Probability distribution is usually technical / academic in register.
Probability distribution: in British English it is pronounced /ˌprɒb.əˌbɪl.ə.ti ˌdɪs.trɪˈbjuː.ʃən/, and in American English it is pronounced /ˌprɑː.bəˌbɪl.ə.t̬i ˌdɪs.trɪˈbjuː.ʃən/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “The dice are loaded (informal metaphor for a non-uniform distribution).”
Learning
Memory Aids
Mnemonic
Think of a 'PROBABILITY DISTRIBUTION' as a 'DISTRIBUTION' of 'PROBABILITY' tickets to different event outcomes. The shape of the distribution shows which outcomes got the most tickets.
Conceptual Metaphor
A map of chances; A landscape of likelihood; A recipe for randomness.
Practice
Quiz
Which of the following is NOT typically a characteristic described by a probability distribution?