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Definitions I (Discrete)


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Sample space (Ω)
Set of all possible outcomes of a random experiment.
Event
A subset of the sample space Ω.
Elementary (or atomic) event
An element of the sample space Ω viewed as event.
Mutually exclusive events
Two events that are disjoint as sets (i.e. their intersection is empty).
Power set
The set ℘(A) of all subsets of a given set A.
Additive function
A function P : ℘(Ω) → R satisfying P(A∪B) = P(A) + P(B) for all disjoint A, B ⊂ Ω.
Probability distribution (finite)
An additive function P from the powerset ℘(Ω) of a finite set Ω to [0,1] such that P(Ω) equals 1.
Countable set
A set with the same cardinality (number of elements) as some subset of the set of natural numbers.
Probability mass function (PMF)
A function P : Ω → [0,1] for a countable Ω such that the sum of the P(ω) over all ω in Ω equals 1.
Discrete probability space
A pair (Ω,P) of a non-empty countable sample space Ω and a probability distribution or mass function P.