Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Cumulative distribution function of a real random variable
Definition
Let be a real random variable. Its cumulative distribution function is the function
The second expression is the same quantity written in terms of the law Law or distribution of a random element of .
Depends on
Used by
- A distribution function need not have a density Counterexample
- Atoms and continuity points of a law Definition
- Discrete, continuous, and mixed distribution functions Example
- Recovering an exponential law from its tail Example
- The uniform random variable on [0,1] Example
- Probability laws correspond to distribution functions Theorem
Dependency tree · two levels
3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- J. R. Norris, Probability and Measure, Section 2.3 (standard reference, not scraped)
- Jean-Francois Le Gall, Integration, Probabilities and Stochastic Processes, Section 8.1.6 (standard reference, not scraped)