Probability Axioms
In probability theory, the probability P of some event E, denoted, is usually defined in such a way that P satisfies the Kolmogorov axioms, named after the famous Russian mathematician Andrey Kolmogorov, which are described below.
These assumptions can be summarised as: Let (Ω, F, P) be a measure space with P(Ω)=1. Then (Ω, F, P) is a probability space, with sample space Ω, event space F and probability measure P.
An alternative approach to formalising probability, favoured by some Bayesians, is given by Cox's theorem.
Read more about Probability Axioms: First Axiom, Second Axiom, Third Axiom, Proofs, More Consequences
Famous quotes containing the words probability and/or axioms:
“The source of Pyrrhonism comes from failing to distinguish between a demonstration, a proof and a probability. A demonstration supposes that the contradictory idea is impossible; a proof of fact is where all the reasons lead to belief, without there being any pretext for doubt; a probability is where the reasons for belief are stronger than those for doubting.”
—Andrew Michael Ramsay (1686–1743)
““I tell you the solemn truth that the doctrine of the Trinity is not so difficult to accept for a working proposition as any one of the axioms of physics.””
—Henry Brooks Adams (1838–1918)