Probability distribution
In probability theory and statistics, a probability distribution describes how probabilities are assigned to the possible results of a random phenomenon—more precisely, to events, which are sets of possible outcomes of a probabilistic experiment.
At a glance
Key signals
0% cross fields · reaches 2 more
- Mathematics
- Statistics
- Probability
- Explanation
- Examples
- Misconception
- Sourced relations 8
- Attribution
Dependencies
What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.
Foundations · builds on
Probability distributiondepends onProbabilityEstablished
probability distribution depends on Probability.
Mechanism: A probability distribution assigns a probability to every possible outcome of a random process.
- Wikipedia (English & German editions) verifiedmoderate evidence
Enables · leads to
Expectationdepends onProbability distributionEstablished
expectation depends on probability distribution.
Mechanism: The expected value is the long-run average of a random variable, weighting each outcome by its probability.
- Wikipedia (English & German editions) verifiedmoderate evidence
Random variabledepends onProbability distributionEstablished
random variable depends on probability distribution.
Mechanism: A random variable is described by its probability distribution: the distribution states how likely each of its values is.
- Wikipedia (English & German editions) verifiedmoderate evidence
System context
Normal distributionis aProbability distributionEstablished
normal distribution is a kind of probability distribution.
Mechanism: The normal distribution is the bell-shaped curve that emerges whenever many small independent effects add up.
- Wikipedia (English & German editions) verifiedmoderate evidence
Structural role & consequence
Interpreted from the current atlas graph — what the connections mean, not just how many there are.
Currently dark in the atlas: no key date stored · 8 of 8 of its relations lack claim-level evidence.
atlas representation · Describes the current Thinking OS representation, not the state of the world.
Builds on 1 foundation (requires / depends-on / derived-from / emerges-from).
structural · Structural graph analysis — not a claim of importance, causation or history.
Structural neighbourhood: 8 → 32 → 111 concepts reachable within 3 hops.
structural · Structural reach — being reachable is not the same as being understood.
All 8 of its relationships stay within its own discipline — a field-specific concept in the current atlas.
structural · Structural graph analysis — not a claim of importance, causation or history.
cross-field
8 within-field, 0 cross-field
Strengths & constraints
Constraints
- Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
- No dated history stored — the atlas records no key date for this concept. atlas representation
Conditions
- Its dependency reading rests on 1 foundation relation. structural
- Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural
Dependency radial
What this concept builds on (left) and what it makes possible (right) — derived from dependency and causal relations.
What builds on this
2 concepts build on this directly, 2 in total, across 2 disciplines.
Structural downstream reach along dependency edges — not a claim of historical necessity.
Seen through each discipline
How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.
Through this lens it connects to Probability, Average, Sampling and Variance.
Through this lens it connects to Probability, Average, Sampling and Variance.
Through this lens it connects to Probability, Random variable, Expectation and Normal distribution.
Check yourself
A quick check against a common misconception. Nothing is scored — picking the tempting-but-wrong answer just flags an idea worth revisiting.
Which statement is correct?
Every outcome in a distribution is equally likely.
Only a uniform distribution is even; most distributions concentrate probability on some outcomes far more than others — that unevenness is the whole point.
Look for: Learner assumes any random outcome has the same probability as any other.
Related ideas to explore
Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.
This idea also appears in…
The same structure shows up in other disciplines. These are real recurrences drawn from the graph — a starting point for asking “what carries over, and what changes?”
Probability24 disciplines · 17 concepts
Concepts
shares a mental model
shares a mental model
shares a mental model
shares a mental model
shares a mental model
shares a mental model
A probability distribution lists all the possible outcomes of something random and how likely each one is. For a fair die it says each of the six faces has a 1-in-6 chance. All the chances together always add up to 1.
A probability distribution assigns a probability to each value a random variable can take, summing (or integrating) to 1. Its shape — its mean and spread — summarises the randomness and lets you compute the chance of any range of outcomes.
Mental models at work here
- Connects 8 other ideas across 3 disciplines.
- A cross-disciplinary bridge — its connections reach into 2 other fields.
- Most of its connections are of the “Dependency” kind.
- It exercises 1 reusable thinking pattern.
Derived from the graph’s real structure — observations, not a score.
Sources
- Wikipedia (English & German editions) verifiedmoderate evidence
- Wikidata verifiedmoderate evidence
- Invariant distribution of Chow statistics (1992) verified
- Limiting distribution of the G statistics (2008) verified