Definition: Kolmogorov axioms of probability
Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Probability axioms ▷ Axioms of probability
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Metadata: ID: D158 | shortcut: prob-ax | author: JoramSoch | date: 2021-07-30, 11:11.
Definition: Let there be a sample space $\Omega$, an event space $\mathcal{E}$ and a probability measure $P$, such that $P(E)$ is the probability of some event $E \in \mathcal{E}$. Then, we introduce three axioms of probability:
- First axiom: The probability of an event is a non-negative real number:
- Second axiom: The probability that at least one elementary event in the sample space will occur is one:
- Third axiom: The probability of any countable sequence of disjoint (i.e. mutually exclusive) events $E_1, E_2, E_3, \ldots$ is equal to the sum of the probabilities of the individual events:
- A.N. Kolmogorov (1950): "Elementary Theory of Probability"; in: Foundations of the Theory of Probability, p. 2; URL: https://archive.org/details/foundationsofthe00kolm/page/2/mode/2up.
- Alan Stuart & J. Keith Ord (1994): "Probability and Statistical Inference"; in: Kendall's Advanced Theory of Statistics, Vol. 1: Distribution Theory, ch. 8.6, p. 288, eqs. 8.2-8.4; URL: https://www.wiley.com/en-us/Kendall%27s+Advanced+Theory+of+Statistics%2C+3+Volumes%2C+Set%2C+6th+Edition-p-9780470669549.
- Wikipedia (2021): "Probability axioms"; in: Wikipedia, the free encyclopedia, retrieved on 2021-07-30; URL: https://en.wikipedia.org/wiki/Probability_axioms#Axioms.
Metadata: ID: D158 | shortcut: prob-ax | author: JoramSoch | date: 2021-07-30, 11:11.