Probability axioms

The probability mathbb{P} of some event E (denoted mathbb{P}(E)) is defined with respect to a "universe" or sample space Omega of all possible elementary events in such a way that mathbb{P} must satisfy the Kolmogorov axioms.

Related Topics:
Probability - Event - Sample space - Elementary event

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Alternatively, a probability can be interpreted as a measure on a σ-algebra of subsets of the sample space, those subsets being the events, such that the measure of the whole set equals 1. This property is important, since it gives rise to the natural concept of conditional probability. Every set A with non-zero probability defines another probability

Related Topics:
Measure - σ-algebra - Conditional probability

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: mathbb{P}(B ert A) = {mathbb{P}(B cap A) over mathbb{P}(A)}

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on the space. This is usually read as "probability of B given A". If the conditional probability of B given A is the same as the probability of B, then B and A are said to be independent.

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In the case that the sample space is finite or countably infinite, a probability function can also be defined by its values on the elementary events {e_1}, {e_2}, ... where Omega = {,e_1, e_2, ...,}.,

Related Topics:
Finite - Countably

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