Experiment (Probability Theory)¶
A mathematical model of a repeatable trial whose possible outcomes form a sample space, measurable events form a sigma-algebra, and probabilities are assigned by a measure.
Core Idea¶
In probability theory an experiment specifies what one trial can produce. Mutually exclusive complete outcomes form Ω; measurable events are sets in F; and P assigns probabilities satisfying the axioms. One ω occurs on a trial, while every event containing ω is said to occur.
Repeated trials can be analyzed separately or composed into a larger experiment whose outcomes are sequences. Repeatability is a modeling ideal, not a claim that physical conditions can be reproduced infinitely exactly.
Scope of Application¶
- Games of chance. Tosses, draws, and rolls give finite spaces.
- Reliability. System states and failures define outcomes and events.
- Statistical sampling. Observed data are outcomes under a sampling model.
- Stochastic processes. Path spaces treat whole trajectories as outcomes.
Clarity¶
State procedure, granularity, Ω, F, and P. The same physical act can support several experiments depending on what is observed. Independence belongs to a joint probability model, not to repetition alone. This distinction is operationally important. Inclusion test: Specify the repeatable procedure and probability space (Ω,F,P), with outcomes distinguished from events and repetitions distinguished from the composed experiment. Exclusion test: Exclude a laboratory study merely called an experiment, an outcome list without probabilities, overlapping elementary outcomes, and empirical frequencies silently equated with a model. Nearest boundary: A trial is one execution; a composed experiment can collect many trials into one larger outcome tuple. Exit condition: The object changes when its procedure, outcome granularity, event algebra, or probability assignment changes.
Manages Complexity¶
A probability space compresses repeatable uncertainty into outcomes, sets, and a measure, enabling many questions without rerunning the procedure. The abstraction hides model misspecification and dependence unless tested.
Abstract Reasoning¶
- Define one execution and observation rule.
- Enumerate or characterize mutually exclusive complete outcomes.
- Choose a sigma-algebra of meaningful events.
- Assign and justify P.
- For repetitions, construct the joint space and state dependence.
Knowledge Transfer¶
The model transfers wherever uncertainty can be represented by a probability space. Calling an uncertain episode an experiment is insufficient until outcomes and measure are supplied.
Relationships to Other Abstractions¶
Current abstraction Experiment (Probability Theory) Domain-specific
Parents (1) — more general patterns this builds on
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Experiment (Probability Theory) presupposes Probability measure Domain-specific
A Probability-Theory Experiment presupposes a Probability Measure because its events receive countably additive probabilities totaling one on the sample space.
Hierarchy paths (2) — routes to 2 parentless roots
- Experiment (Probability Theory) → Probability measure → Probability → Measure → Aggregation → Micro Macro Linkage
- Experiment (Probability Theory) → Probability measure → Probability → Measure → Set and Membership
Neighborhood in Abstraction Space¶
Experiment (Probability Theory) sits in a crowded region of the domain-specific corpus (33rd percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Decision & System Modeling Frameworks (30 abstractions)
Nearest neighbors
- Misuse of p-values — 0.90
- Probability matching — 0.90
- Funnel Chart — 0.88
- Stochastic Grammar — 0.88
- N-of-1 Trial — 0.88
Computed from structural-signature embeddings · 2026-10-08