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Probability Axioms


Given an event E in a sample space S which is either finite with N elements or countably infinite with N=infty elements, then we can write

 S=( union _(i=1)^NE_i),

and a quantity P(E_i), called the probability of event E_i, is defined such that

1. 0<=P(E_i)<=1.

2. P(S)=1.

3. Additivity: P(E_1 union E_2)=P(E_1)+P(E_2), where E_1 and E_2 are mutually exclusive.

4. Countable additivity: P( union _(i=1)^nE_i)=sum_(i=1)^(n)P(E_i) for n=1, 2, ..., N where E_1, E_2, ... are mutually exclusive (i.e., E_1 intersection E_2=emptyset).


See also

Experiment, Independence Axiom, Kolmogorov's Axioms, Outcome, Probability, Sample Space, Trial, Union

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References

Doob, J. L. "The Development of Rigor in Mathematical Probability (1900-1950)." Amer. Math. Monthly 103, 586-595, 1996.Papoulis, A. Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, pp. 26-28, 1984.

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Probability Axioms

Cite this as:

Weisstein, Eric W. "Probability Axioms." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ProbabilityAxioms.html

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