Questions tagged [kolmogorov-axioms]

Constitute Kolmogorov's mathematical definition of a probability space. It is a triplet $(\Omega, \mathcal F, P)$ where $P$ has to satisfy three axioms: non-negativity, adding to one, and countable addivity.

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Explain to my intuition: New axioms for rigorous Bayesian probability

I stumbled upon this very interesting article : New axioms for rigorous Bayesian probability https://projecteuclid.org/euclid.ba/1340369856 Whose aim is to provide new axioms for probability theory ...
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Axiomatized formal foundation of statistics

I'm learning statistics in foreign language. Being aware of possibly different foundations (e.g. frequentists v.s. Bayesian), I hope to acquire one formally axiomatized foundation of statistics. That ...
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Can we get uniform distributions on infinite spaces by giving up infinite additivity

I am wondering whether it is possible to translate the idea of drawing a number randomly from the set of all natural numbers. If we have infinite additivity as an axiom this obviously does not work. ...
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Is it necessary for the random variables to be defined on the same sample space to calculate joint distribution function?

Is it necessary for the random variables say X and Y to be defined on the same sample space to calculate their joint distribution function? I do not think so though I read it that way in a book.